# How do you solve the system y=1/2x+4 and y=-4x-5 by graphing?

Mar 17, 2016

The equations are in standard form, $y = m x + c$, where $m$ is the slope (gradient) and $c$ is the y-intercept. Using this, graph as shown below to find the solution $\left(- 2 , 3\right)$.

#### Explanation:

The solution of this set of simultaneous linear equations is the point where the lines cross.

You can read from the graph that this point is $\left(- 2 , 3\right)$.

The equations can also be solved algebraically (as a way of checking your answer) by equating the two equations with one another:

$\frac{1}{2} x + 4 = - 4 x - 5$

Double to make it neater:

$x + 8 = - 8 x - 10$

Add $8 x$ both sides and subtract 8 from both sides:

$9 x = - 18$ which gives $x = - 2$

Substitute back into either equation to find $y = 3$.