Algebra and proofAdditional / Further Maths

Solving simultaneous equations - by substitution

Substitute one expression for a variable into the other equation.

  • Isolate a variable in one equation.
  • Substitute the entire expression, using brackets when needed.
  • Solve, then substitute back to find the other variable.

Example

Replace by

Solve the simultaneous equations by substitution.

Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.

Your turn

Question 1

Solve the simultaneous equations.

Check answer
Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.
Question 2

Solve the simultaneous equations.

Check answer
Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.
Question 3

Solve the simultaneous equations.

Check answer
Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.
Question 4

Solve the simultaneous equations.

Check answer
Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.
Question 5

Solve the simultaneous equations.

Check answer
Make the subject of the first equation. Substitute this expression into the second equation.Expand and collect like terms after substitution.Subtract from both sides, then divide both sides by .Substitute this value into .Evaluate and record the pair. Check it in both original equations.
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