# G7

Example: Find the solution to the following simultaneous equations using graphs.

y=3x -2 (1)

2y=2x-2(2)

Solution: To find the solution to simultaneous equations using graphs, we want to plot both the graphs and see where they cross. The coordinates of the crossing point will be the solution. So, firstly, we want to fill out the table for equation (1) by substituting the $x$ values in. Doing this, we get

Now, for equation (2), we have to rearrange it to make $y$ the subject before substituting any values in. So, if we divide both sides by 2, we get

$y=x-1$

So, substituting $x$ values into this equation, we get the filled out table:

Now we want to plot each set of these coordinates, joining up the points to form a pair of lines representing our simultaneous equations.

Looking at the graph, we can see that the lines meet at (0.5, -0.5). So, the solution is

$x=0.5,\,\,y=-0.5$