Question

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

Answer 1

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

Explanation:

To solve the system of equations by graphing `5x−8y=2` and `2x+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=2x+8` is already in this form, with `y`-intercept being at `(0,8)`. As slope is `2`, other point could be `(0-4,8-8)` or `(-4,0)`

Similarly draw the second line, which in slope-intercept form is `y=(5/8)x-2/8`. Alternatively random trials show that `(2,1)` and `(10, 6)` 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 `(-6, -4)`.