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Solve Simultaneous Equations Graphically

In this worksheet, students will practise solving simple simultaneous equations graphically by finding the point of intersection on an x-y graph.

'Solve Simultaneous Equations Graphically' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Algebra

Curriculum subtopic:   Understand Expressions, Equations, Inequalities, Terms and Factors

Difficulty level:  

Worksheet Overview

Simultaneous equations can be solved by drawing the line representing each equation and then finding the point of intersection between the two lines.


Use y = mx + c, or other methods, to draw the lines.



By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 2

x + y = 3



y = x + 2 has a gradient of 1 and an intercept on the y-axis at (0, 2)


x + y = 3 can be rearranged to read 

y = 3 - x which has a gradient of -1 and an intercept on the y-axis at (0, 3)


The lines are drawn on a set of coordinate axes.


coordinate axis


The point of intersection is (½, 2½) and this is the only point at which both equations are satisfied. We can also write this as (0.5, 2.5)


So the solution to the simultaneous equations is x = 0.5, y = 2.5

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