The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

Solving simultaneous linear equations graphically

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 A and B are simultaneous equations such that A: $$x + 2y = 21$$ and B: $$3x + y = 43$$ where will coordinate pair $$(1, 10)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$2x + 2y = 10$$ and B: $$3x + y = 7$$ where will coordinate pair $$(1, 4)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$2y - 2x = 8$$ and B: $$3x + y = 4$$ where will coordinate pair $$(0, 0)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$3x + y = 40$$ and B: $$7x + y = 88$$ where will coordinate pair $$(12, 4)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$3x + y = 13$$ and B: $$7x + 6y = 34$$ where will coordinate pair $$(5, -2)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$3x + y = 9$$ and B: $$4x +3y = 7$$ where will coordinate pair $$(1, 1)$$ go in the Venn diagram? 

Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 32$$ and $$x + 3y = 17$$?

Using substitution, what is the value of $$x$$ for simultaneous equations $$6x + 4y = 64$$ and $$x + 3y = 34$$?

Using substitution, what is the value of $$y$$ for simultaneous equations $$10x + 8y = 56$$ and $$x + 3y = 10$$?

Using substitution, what is the value of $$y$$ for simultaneous equations $$14x + 4y = 6$$ and $$2x = 3 - y$$?

Using substitution, what is the value of $$y$$ for simultaneous equations $$14x + 4y = 72$$ and $$2x + y = 15$$?

Using substitution, what is the value of $$y$$ for simultaneous equations $$2y - 2x = -2$$ and $$3x + y = 19$$?

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

Solving simultaneous linear equations graphically

Lesson outcome

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