We are given the following system of equations:
[tex]\begin{gathered} 6x-5y=34,(1) \\ 3x+2y=8,(2) \end{gathered}[/tex]We are asked to verify if the point (-36, 58) is a solution to the system. To do that we will substitute the values x = -36 and y = 58 in both equations and both must be true.
Substituting in equation (1):
[tex]6(-36)-5(58)=34[/tex]Solving the left side we get:
[tex]-506=34[/tex]Since we don't get the same result on both sides this means that the point is not a solution.
Now, we will determine where was the mistake.
The first step is to solve for "y" in equation (2). To do that, we will subtract "3x" from both sides:
[tex]2y=8-3x[/tex]Now, we divide both sides by 2:
[tex]y=\frac{8}{2}-\frac{3}{2}x[/tex]Solving the operations:
[tex]y=4-1.5x[/tex]Now, we substitute this value in equation (1), we get:
[tex]6x-5(4-1.5x)=34[/tex]Now, we apply the distributive law on the parenthesis:
[tex]6x-20+7.5x=34[/tex]This is where the mistake is, since when applying the distributive law the product -5(-1.5x) is 7.5x and not -7.5x.