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

A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2; the graph of which forms a parabola.

Solving a quadratic and linear pair of simultaneous equations graphically

Maths

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Combining 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 a quadratic and linear pair of simultaneous equations using elimination

Solving a quadratic and linear pair of simultaneous equations using substitution

Solving simultaneous equations via any method

Problem solving with linear and quadratic 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

How many solutions satisfy both equations?

When $$y = 0$$, how many solutions are there for the equation?

What is the positive coordinate pair that solves both $$x^2 + y^2 = 13$$ and $$9x -9y = 9$$?

What is the positive coordinate pair that solves both $$x^2 + y^2 = 17$$ and $$5x - 5y = 15$$?

What is the positive coordinate pair that solves both $$x^2 + y^2 = 40$$ and $$3x - 3y = 12$$?

If equation A is $$x^2 + 4y = 68$$ and equation B is $$2x - 8y = 8$$, which coordinate pair would sit in the intersection of A and B? 

If equation A is $$2x - 10y = -14$$ and equation B is $$x^2 + y^2 = 13$$, which coordinate pair would sit in A and not B? 

If equation A is $$x^2 + 3y = 24 $$ and equation B is $$8x - 6y = -6$$, which coordinate pair would sit in A and not B? 

Solving a quadratic and linear pair of simultaneous equations graphically

Lesson outcome