Respuesta :
Given
[tex]-2x-2y=8[/tex]To find a solution for the linear equation, the first step is to write the equation in slope-intercept form:
-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of the equal sign:
[tex]\begin{gathered} -2x+2x-2y=8+2x \\ -2y=2x+8 \end{gathered}[/tex]-Divide both sides by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{2x}{-2}+\frac{8}{-2} \\ y=-x-4 \end{gathered}[/tex]Once you have expressed the equation of the line in slope-intercept form, replace it with any value for x and calculate the corresponding value of y, for example, x=2
[tex]\begin{gathered} y=-(2)-4 \\ y=-2-4 \\ y=-6 \end{gathered}[/tex]One solution for the linear equation is x=2 and y=-6, you can check the solution by replacing the values on the original equation, with both values the result should be 8:
[tex]\begin{gathered} -2x-2y \\ -2\cdot2-2\cdot(-6) \\ -4+12=8 \end{gathered}[/tex]As you can see the values are a valid solution for the linear equation.
So the solution is:
[tex]-2(2)-2(-6)=8[/tex]