AI generatedAlgebraKS3 / GCSE

Simultaneous equations by substitution

Simultaneous equations by substitution.

  • The same pair of values must satisfy both equations.
  • For elimination, multiply every term of an equation by the same number. For substitution, replace a variable by an equal expression.
  • Substitute the final pair into both original equations to check.

Example 1

Solve the simultaneous equations.

Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .

Example 2

Solve the simultaneous equations.

Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .

Your turn

Question 1

Solve the simultaneous equations.

Check answer
Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .
Question 2

Solve the simultaneous equations.

Check answer
Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .
Question 3

Solve the simultaneous equations.

Check answer
Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .
Question 4

Solve the simultaneous equations.

Check answer
Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .
Question 5

Solve the simultaneous equations.

Check answer
Label this equation (1).Label this equation (2).Subtract from both sides of (1), then substitute this expression for into (2).Expand the brackets and collect the terms.
Substitute this value into .Evaluate to find .
← All Algebra cardsReport a mistake