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

Solving a quadratic and linear pair of simultaneous equations using elimination

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

What is the positive value of $$x$$ for $$x^2 + 3x - 4 = 0$$

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

What is the negative value of $$x$$ for $$2x^2 + 4x - 6 = 0$$

Write the positive coordinate solution for $$x^2 + 3y = 19$$ and $$3x - 3y = -9$$

Write the positive coordinate solution for $$x^2 + 2y = 11$$ and $$3x - 2y = 7$$

Which of these is not a solution for simultaneous equations $$x^2 + 4y = 17$$ and $$2x - 4y = -2$$?

If A and B are simultaneous equations such that A: $$2x + 4y = 42$$ 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: $$4x + 4y = 20$$ and B: $$6x + 2y = 14$$ 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: $$9x + 3y = 12$$ 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: $$14x + 2y = 176$$ where will coordinate pair $$(12, 4)$$ go in the Venn diagram? 

If A and B are simultaneous equations such that A: $$6x + 2y = 26$$ 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: $$6x = 18 - 2y$$ and B: $$8x +6y = 14$$ where will coordinate pair $$(1, 1)$$ go in the Venn diagram? 

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

Solving a quadratic and linear pair of simultaneous equations using elimination

Lesson outcome

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