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

1 Answer
Feb 16, 2016

Answer:

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)#.