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

Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.

Solving simultaneous equations via any method

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

Solve using any method: $$3x + 5y = -6$$ and $$5x - 5y = 30$$. Write your answer in the form $$(x,y)$$.

Solve using any method: $$3x + y = 15$$ and $$5x - 5y = 45$$. Write your answer in the form $$(x,y$$).

Solve using any method: $$6x + 2y = 30$$ and $$6x - 5y = 51$$. Write your answer in the form $$(x,y)$$.

Solve using any method: $$8x + 2y =10$$ and $$3x - 4y = 18$$. Write your answer in the form $$(x,y)$$.

Solve using any method: $$x + 5y =24$$ and $$5x + 3y = 10$$. Write your answer in the form $$(x,y)$$.

Solve using any method: $$5x + 4y = 11$$ and $$2x + 5y = 35$$. Write your answer in the form $$(x,y)$$.

Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 32$$ and $$3x + 9y = 51$$?

Using substitution, what is the value of $$x$$ for simultaneous equations $$7x + 2y = 36$$ and $$4x + 2y = 30$$?

Using substitution, what is the value of $$y$$ for simultaneous equations $$y - x = -1$$ and $$3x + y = 19$$?

Which multiplier would match the x coefficients for equations 1) $$6x + 10y = 42$$ and 2) $$x + 2y = 8$$:

What is the value of $$y$$ for simultaneous equations $$x + 4y = 7$$ and $$2x + 3y = -1$$

What is the value of $$x$$ for simultaneous equations $$x + y = 7$$ and $$6x + 3y = 27$$

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

Solving simultaneous equations via any method

Lesson outcome

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