Question

What is the y value of the solution to the system of equations shown below y = 22 - 6 y = 50 – 21

Answer 1

Given the equation system:

`\begin{cases}y=2x-6 \\ y=5x-21\end{cases}`

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:

`2x-6=5x-21`

-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:

`\begin{gathered} 2x-5x-6=5x-5x-21 \\ -3x-6=-21 \end{gathered}`
`\begin{gathered} -3x-6+6=-21+6 \\ -3x=-15 \end{gathered}`

-Divide both sides by -3 to reach the value of x:

`\begin{gathered} -(3x)/(-3)=-(15)/(-3) \\ x=5 \end{gathered}`

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

`\begin{gathered} y=2x-6 \\ y=2\cdot5-6 \\ y=10-6 \\ y=4 \end{gathered}`

So the corresponding y value for the solution of this equation system is y= 4 (option D)