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

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

Checking and securing understanding of interpreting graphs

Maths

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 a quadratic and linear pair of simultaneous equations graphically

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

Which of the following coordinate pairs satisfies the equation $$2x + 5y = 58$$? 

Which of the following coordinate pairs satisfies the equation $$6x + 2y = 26$$? 

Which of the following coordinate pairs satisfies the equation $$5x = 1 - 2y$$? 

Which of the following coordinate pairs satisfies the equation $$5x + 2y = 54$$? 

If $$x = 2$$, what is the value of $$y$$ for  $$5x + 2y = -8$$? 

If $$x = 2$$, what is the value of $$y$$ for  $$5x + 2y = 32$$? 

Which pair of coordinates does not sit on the line $$y = 2x + 1$$?

Which point is not on the line represented by $$y = -x - 2$$?

Which of these coordinates does not lie on the line $$y = 0.5x + 2$$?

Which pair of coordinates is not a solution to the equation $$x^2 - y^2 = 16$$?

Which coordinate pair does not satisfy the quadratic equation $$y = x^2 - 4x + 3$$?

Which point does not satisfy the equation $$2x^2 + 3x - 5 = y$$?

Checking and securing understanding of interpreting graphs

Lesson outcome