Systems by substitution
Systems by substitution
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Total answers
Solve the system. Find the values of x and y.
y = 2x − 1
x + y = 5
What does the generator do?
It builds a 2×2 linear system with one equation solved for y and a whole-number solution, and asks for x and y.
How to solve
Replace y in the second equation with the expression from the first, solve the resulting one-variable equation, then substitute back.
Other exercise generators:
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- Addition within 100 — with regrouping
- Addition & subtraction within 20
- Angle from a circle
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- Measure an angle with a protractor
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- Angle sum in a triangle
- Vertical and supplementary angles
- Alternate angles on parallel lines
- Corresponding angles on parallel lines
- Area by counting squares
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- Axes of symmetry of a shape
- Read a bar chart
- Bar charts (advanced)
- Second binomial formula — expand (ax − b)²
- Recognize the binomial formula
- Third binomial formula — (ax − b)(ax + b)
- First binomial formula — expand (ax + b)²
- Compare two box plots
- Pick the correct box plot for the data
- Read values off a box plot
- Building Blocks
- Point symmetry — find the image of a point
- Area of a circle from the radius
- Word problem — area of a circle
- Circumference of a circle from the radius
- Find the radius from the circumference
- Classify the quadrilateral
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- Column addition — two-digit
- Column addition — 3 digits
- Column addition — 4-digit numbers
- Column subtraction — 3 digits
- Column subtraction — 4-digit numbers
- Compare the number of balls
- Compare two line graphs
- Compare integers
- Comparing Numbers
- Comparing within 100
- Compare numbers to 1,000
- Compare numbers up to 10,000
- Comparing within 20
- Compare large numbers
- Comparing Powers
- Compare scientific notation
- Complete the symmetric figure
- Perimeter and area of composite figures
- Cone Surface Area
- Cone Volume
- Count back through zero
- Combinations — tree diagram
- Counting Tens
- Counting tens
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- Cube buildings – mixed
- Total number of cubes
- Count visible cubes
- Cube net
- Cube root (perfect cube)
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- Cylinder Surface Area
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- Add and subtract decimals
- Compare decimals
- Divide a decimal by a decimal
- Divide a decimal by a whole number
- Decimals and fractions
- Multiply and divide decimals by 10, 100, 1000
- Multiply a decimal by a whole number
- Decimal on a number line
- Decimal place value
- Recurring or terminating decimal?
- Round decimals
- Decompose Powers into Product
- Digit at a given place
- Which digit is in the …?
- Distance between two points on a gridline
- Divide by 10, 100, 1000
- Long division
- Long division by a two-digit number
- Long division with remainder
- Divisibility rules
- Dividing by 2, 5, 10
- Division as sharing
- Fact families
- Reading dot plots
- Read a double bar graph
- Draw a polygon from coordinates
- Equation Solver
- Distributive property – equivalent expressions
- Evaluate an expression
- Evaluating expressions
- Evaluate an expression with two variables
- Evaluate a root expression
- Expand using the distributive property
- Expanded form
- Expanded form (up to 10,000)
- Expanded form (up to a million)
- Combining Like Terms
- Equivalent Expressions
- Evaluating Expressions
- Expanding Parentheses
- Factoring Out
- Algebraic Fractions
- Multiplying by a Monomial
- Cube of a Binomial
- Multiplying Binomials
- Substitution into Expressions
- Factor out a common factor
- All factors of a number
- Find the Correct Exercise
- Find the missing number to 1,000
- Find the Bigger or Smaller Number
- Integer expressions (order of operations)
- Fraction, decimal and percent — the same thing in three forms
- Divide a fraction by a fraction
- Fractions — multi-step expressions
- Name the fraction
- Fraction of a set
- Fraction of a set
- Write the fraction
- Shade the fraction
- Add fractions with different denominators
- Add fractions (same denominator)
- Compare fractions
- Equivalent fractions
- Multiply a fraction by a whole number
- Fraction of a number
- Subtract fractions with different denominators
- Subtract fractions (same denominator)
- Direct Proportion
- Domain of a Function
- Inverse Proportion
- Linear Function
- Range of a Function
- Reading from Graph
- Function Table
- Dependent and Independent Variables
- Greatest common factor (GCF)
- Reading histograms
- Find a number up to 100
- Linear Inequalities - Basic
- Inequalities - Variable on Both Sides
- Inequalities - Intervals
- Inequalities - Mixed Problems
- Inequalities - Number Line
- Inequalities - Special Cases
- Inequalities with Fractions
- Inequalities with Parentheses
- Do we need brackets?
- Inverse rule of three
- Least common multiple (LCM)
- Compare lengths in different units
- Compare lengths
- Compare lengths in mixed units
- Compare lengths
- Convert from a larger unit to a smaller one
- Length: convert down
- Convert from a smaller unit to a larger one
- Length: convert up
- Fill in the unit
- Length: fill the missing unit
- Compare imperial units
- Imperial length: compare
- Imperial units – larger to smaller
- Imperial length: convert down
- Imperial units – smaller to larger
- Imperial length: convert up
- Arithmetic with mixed units
- Convert two units to one
- Length units
- Length units — cm and m
- Line of best fit
- Line plot with fractions
- Word problem with a linear equation
- Linear Equations - Basic
- Linear Equations - Both Sides
- Unknown in Denominator on Both Sides
- Unknown on Both Sides with Fractions
- Equivalent Equations
- Equations with Fractions - Unknown in Denominator
- Equations with Fractions - Unknown in Numerator
- Linear Equations - Number of Solutions
- Equations with Plus on One Side
- Equations with Two Plus Terms
- One-step linear inequality
- Arrangements — systematic listing
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- Mean (Average)
- Comparing measurements
- Median
- Mixed number ↔ improper fraction
- Mixed and improper fractions
- Mode
- Coin combinations
- Combine coins
- Count the money
- Count money
- Euros and cents — decimal notation
- Making change
- Make change
- Money word problems
- Money word problems
- Multiples of a number
- Multiplication and Division Exercises
- Times tables 2, 5, 10
- Multiplication as an array
- Multiplication as an array — review
- Multiplication as addition
- Times tables — quick drill
- Find the missing factor
- Fill the missing times-table cell
- Times tables 1 to 12
- Multiplication word problems
- Times-tables word problems
- 2-digit × 2-digit multiplication
- Multiply and divide by 10, 100, 1000
- Column multiplication up to 10,000
- Multi-digit × 1-digit multiplication
- Long multiplication with multi-digit numbers
- Multiply and divide integers
- Multiplying a round number by a one-digit number
- Multiplying a round number by the same digit
- Negative number on a number line
- Number Line
- Number Line up to 10
- Number on a 0–100 line
- Number line to 1,000
- Number Chain
- Addition Pyramid
- Number Series Completion
- One-step equations – add and subtract
- One-step equations – multiply and divide
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- Order Numbers
- Order numbers to 100
- Order numbers to 1,000
- Order Numbers up to 10,000
- Order of operations — with brackets
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- Multi-step problems — order of operations
- Choosing pairs
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- Reading pie charts
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- Tens and ones
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- Addition and Subtraction with Numbers Up to 10,000
- Addition and Subtraction Patterns up to 10,000
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- Classify polygons
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- Sides and vertices
- Direction and turns
- Power laws (same base)
- Powers
- Powers Calculation
- Powers and decimal places
- Powers Simplification
- Powers with Fractions
- Powers with Letters
- Powers with Unknown Exponent
- exercises.prima-01-length-units.title
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- exercises.prima-07-circles-in-circle.title
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- exercises.prima-11-rounding-pair.title
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- exercises.prima-13-remainder-error.title
- exercises.prima-14-strike-out-digits.title
- exercises.prima-15-tallest-building.title
- exercises.prima-16-hidden-digits.title
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- Prime or composite?
- Volume of a prism — from base area and height
- Compound event — coin and die
- Experimental vs theoretical probability
- Probability of a simple event
- Per mille (‰) — introduction
- Read from a proportion graph
- Rule of three — direct proportion
- Pyramid Surface Area
- Pyramid Volume
- Pythagorean theorem — find the hypotenuse
- Pythagorean theorem — find a leg
- Pythagorean Theorem – Find the Hypotenuse
- Pythagorean Theorem – Find a Leg
- Pythagorean Theorem – Mixed Practice
- Verify a Right Triangle
- Pythagorean Theorem – Word Problems
- Word problem — ladder against a wall
- Name the quadrilateral
- Quartiles — compute Q1, median and Q3
- Random sample — estimating the population
- Range
- Equivalent ratio — fill in the missing term
- Ratio in simplest form
- Rational or irrational?
- Read coordinates of a point
- Read coordinates — all four quadrants
- Read a line graph
- Reading a ruler
- Recipe — how much of each ingredient?
- Reflect a point
- Right angles
- Right, acute and obtuse angles
- Roman numerals — mixed
- Read Roman numerals
- Write Roman numerals
- Rounding large numbers
- Round large numbers
- Round to the nearest 10 and 100
- Round 4-digit numbers
- Sample space — list all outcomes
- Savings — final balance
- Map scale
- Scatter plots — association
- Scientific notation → standard form
- Find the shapes
- Find the shape in the picture
- Name the shape
- Name the shape
- Name the shape
- Operations on signed fractions
- Triangle Similarity – Missing Side
- Triangle Similarity – Mixed Problems
- Triangle Similarity – Similarity Ratio
- Triangle Similarity – Similarity Theorems
- Simple interest
- Simplifying exponents
- Simplify a linear expression
- Skip counting
- Faces, edges, and vertices
- Faces, edges, vertices
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- Objects around us
- Surface Area & Volume - Mixed
- Recognising solids – mixed
- Solve p · (x + q) = r
- Solve px + q = r
- Unknown on both sides
- Sphere Surface Area
- Sphere Volume
- Area of square and rectangle
- Area of squares and rectangles
- Perimeter of square and rectangle
- Perimeter of squares and rectangles
- Estimate a square root
- Square root (perfect square)
- Subtraction within 100 — no borrowing
- Subtraction within 100 — with borrowing
- Line of symmetry
- Line of symmetry
- Lines of symmetry
- Systems by elimination
- Systems from word problems
- Solve a system from a graph
- Read a tally chart
- Tally charts (advanced)
- Temperature word problem
- Tens and ones
- Thales's theorem — construct a right triangle
- Thales's theorem — find the right angle
- Thales's theorem — tangent from a point
- Equations with three members
- Clock — to the minute
- Clock to 5 minutes
- Read the clock — to any minute
- Telling time — full hours
- Clock — whole hours (review)
- Hours and minutes conversion
- Time: convert units
- Days of the week and months
- Elapsed time
- Elapsed time problems
- Area of a trapezoid
- Perimeter of a trapezoid
- Area of triangle
- Triangle congruence criterion
- Perimeter of triangle
- Volume of a triangular prism
- Two-way tables
- Unit rate
- Converting units of volume
- Volume units — ml and l
- Capacity: convert millilitres and litres
- Weight units
- Weight units — g and kg
- Mass: convert grams and kilograms
- Word problems to 1,000
- Word problems — add and subtract to 1000
- Word problems — addition
- Word problems
- Word problems — compare and total
- Comparison word problems
- Word problems with decimals
- Word problems — division
- Division word problems
- Word problems with fractions
- Word problems — multiplication
- Multiplication word problems
- Word problems — two steps
- Multi-step word problems
- Multi-step word problems
- Multi-step word problem
- Multi-step word problems
- Multi-step word problems — mixed
- Word problems with percentages
- Multi-step percent word problems
- Perimeter and area word problem
- Word problems with ratios
- Word problems with ratios — follow-up
- Word problems with rational numbers
- Rule of three — direct and inverse proportion
- Word problems — subtraction
- Word problem with decimals
- Word problem with fractions
- Match the expression to the words
- Writing expressions with a variable
- Write in scientific notation
- Number of trailing zeros