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.

**Example**

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

**y = x + 2**

x + y = 3

**Answer**

**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.

The point of intersection is (½, 2½) and this is the *only point *at which *both *equations are satisfied.

So the solution to the simultaneous equations is x = ½, y = 2½.