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

Combining equations

Maths

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Solving simultaneous equations by elimination from a context

Solving algebraic simultaneous equations by elimination

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving simultaneous equations via any method

Problem solving with simultaneous equations

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.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

Simultaneous equations: 2 variables

Which equation is true for $$x = 2$$ and $$y = 5$$? 

Which equation is true for $$x = 3$$ and $$y = 9$$? 

Which equation is true for $$x = -2$$ and $$y = 3$$? 

Which equation is true for $$x = 8$$ and $$y = 1$$? 

If I add together the pair of simultaneous equations $$5x + 7y = 87$$ and $$7x + 7y = 91$$, what is the resulting equation? 

If I add together the pair of simultaneous equations $$5x + 2y = 10$$ and $$7x - 2y = -50$$, what is the resulting equation? 

Which pair of coordinates does not satisfy the equation $$y = 2x + 4$$?

The area of a rectangle is $$90 cm^2$$. The perimeter is $$94 cm$$. Which two equations are true for side lengths $$a$$ and $$b$$? 

Which two of the following are correct for a right triangle with sides $$a, b$$ and hypotenuse $$c$$? 

If $$x = -9$$, what is the value of $$y$$ for  $$x + 2y = 13$$? 

Which pair of coordinates does not satisfy the equation $$y = -3x + 2$$?

There are 12 goals scored in a football match. Team A scored $$a$$ goals, and winning Team B scored $$b$$ goals. The winning team scored 5 more than the losing team.

Combining equations

Lesson outcome