AI generatedAlgebraGCSE Higher

Solving linear and quadratic simultaneous equations

Substitute the linear expression into the quadratic relation.

  • 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

Find both intersection points.

Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.

Example 2

Find both intersection points.

Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.

Your turn

Question 1

Find both intersection points.

Check answer
Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.
Question 2

Find both intersection points.

Check answer
Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.
Question 3

Find both intersection points.

Check answer
Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.
Question 4

Find both intersection points.

Check answer
Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.
Question 5

Find both intersection points.

Check answer
Both expressions equal , so set them equal. Subtract from both sides.Factorise.Set each factor equal to zero.Substitute each -value into .Keep each -value paired with its corresponding -value.
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