Given the equation system:
[tex]\begin{cases}y=2x-6 \\ y=5x-21\end{cases}[/tex]
To determine the y-value of the solution of the equation system, first, you have to calculate the value of x.
To determine the value of x, equal both expressions:
[tex]2x-6=5x-21[/tex]
-Pass the x-term to the left side of the equation and the constant to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2x-5x-6=5x-5x-21 \\ -3x-6=-21 \end{gathered}[/tex][tex]\begin{gathered} -3x-6+6=-21+6 \\ -3x=-15 \end{gathered}[/tex]
-Divide both sides by -3 to reach the value of x:
[tex]\begin{gathered} -\frac{3x}{-3}=-\frac{15}{-3} \\ x=5 \end{gathered}[/tex]
Now that you have determined the value of x, replace it in either one of the equations to calculate the corresponding y-value, for example, replace the first equation with x=5
[tex]\begin{gathered} y=2x-6 \\ y=2\cdot5-6 \\ y=10-6 \\ y=4 \end{gathered}[/tex]
So the corresponding y value for the solution of this equation system is y= 4 (option D)
