# How do you solve the system of equations by graphing 5x-8y=2 and 2x+8=y?

Feb 16, 2016

Draw the graphs of two lines (as explained below), whose point of intersection gives the solution, which is $\left(- 6 , - 4\right)$

#### Explanation:

To solve the system of equations by graphing 5x−8y=2 and $2 x + 8 = y$, one needs to draw the graph of two straight lines,

To graph a linear equation, one can convert it into slope and y-intercept form (described by the writer elsewhere). Locate the y-intercept on the graph and plot the point. From this point, use the slope to find a second point and plot it. Draw the line that connects the two points. Here second equation $y = 2 x + 8$ is already in this form, with $y$-intercept being at $\left(0 , 8\right)$. As slope is $2$, other point could be $\left(0 - 4 , 8 - 8\right)$ or $\left(- 4 , 0\right)$

Similarly draw the second line, which in slope-intercept form is $y = \left(\frac{5}{8}\right) x - \frac{2}{8}$. Alternatively random trials show that $\left(2 , 1\right)$ and $\left(10 , 6\right)$ satisfy second equation and hence joining them gives second line.

Coordinates of the point of intersection of the two lines will give solution of the equation, which is $\left(- 6 , - 4\right)$.