We are given the following equation system:
[tex]\begin{gathered} -4x+y=16,(1) \\ -8x+8y=-16,(2) \end{gathered}[/tex]The slope-intercept form of a linear equation is the following:
[tex]y=mx+b[/tex]Taking equation (1):
[tex]-4x+y=16[/tex]Now we solve for "y". To do that we add 4x to both sides:
[tex]\begin{gathered} -4x+4x+y=16+4x \\ y=4x+16 \end{gathered}[/tex]Now, taking equation (2):
[tex]-8x+8y=-16[/tex]Adding 8x to both side:
[tex]\begin{gathered} -8x+8x+8y=-16+8x \\ 8y=8x-16 \end{gathered}[/tex]Dividing both sides by 8:
[tex]\begin{gathered} y=\frac{8x}{8}-\frac{16}{8} \\ y=x-2 \end{gathered}[/tex]The graph of both equations are the following:
Since the graphs of each line do not have the same slope, they are a consistent system and are independent. The solution is the point where the two lines intercept, that is (x,y) = (-6,-8).
