Everything Maths Grade 10

Solving graphically EMA3C

Simultaneous equations can also be solved graphically. If the graphs of each linear equation are drawn, then
the solution to the system of simultaneous equations is the coordinates of the point at which the two graphs
intersect.

For example:

x= 2y : : :(1)

y= 2x 3 : : :(2)

The graphs of the two equations are shown below.

 1 1 2 3

 1

1

2

y= 2x 3

y=^12 x

(2; 1)

x

y

The intersection of the two graphs is(2; 1). So the solution to the system of simultaneous equations isx= 2
andy= 1. We can also check the solution using algebraic methods.

Substitute equation(1)into(2):

x= 2y

)y= 2(2y) 3

Then solve fory:

y 4 y= 3

 3 y= 3

)y= 1

Substitute the value ofyback into equation(1):

x= 2(1)

)x= 2

Notice that both methods give the same solution.

VISIT:

You can use an online tool such asgraphsketchto draw the graphs and check your solution.

86 4.4. Solving simultaneous equations