Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.

Solving a quadratic and linear pair of simultaneous equations using substitution

Maths

In the future unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

Simultaneous equations: 2 variables

If equation A is $$x^2 + 3y = 24 $$ and equation B is $$4x - 3y = -3$$, which coordinate pair would sit in A and not B? 

If equation A is $$x - 5y = -7$$ and equation B is $$x^2 + y^2 = 13$$, which coordinate pair would sit in A and not B? 

If equation A is $$x^2 + 4y = 68$$ and equation B is $$x - 4y = 4$$, which coordinate pair would sit in the intersection of A and B? 

What is the positive coordinate pair that solves both $$x^2 + y^2 = 17$$ and $$x - y = 3$$?

What is the positive coordinate pair that solves both $$x^2 + y^2 = 40$$ and $$x - y = 4$$?

What is the positive coordinate pair that solves both $$x^2 + y^2 = 13$$ and $$x - y = -1$$?

Which of these is not a solution for simultaneous equations $$2x^2 + 8y = 34$$ and $$x - 2y = -1$$?

Write the positive coordinate solution for $$2x^2 + 6y = 38$$ and $$x - y = -3$$

What is the negative value of $$x$$ for $$4x^2 + 8x - 12 = 0$$

What is the value of $$x$$ for $$4x^2 + 8x + 4 = 0$$

What is the negative value of $$x$$ for $$6x^2 + 12x - 18 = 0$$

What is the positive value of $$x$$ for $$2x^2 + 6x - 8 = 0$$

This lesson will be removed by end of Summer Term 2025.

Solving a quadratic and linear pair of simultaneous equations using substitution

Lesson outcome

This lesson will be removed by end of Summer Term 2025.