Question

solve the system of equations. which answer choice has truth to it's solution?y=X+7y=1/4x+11/2multiple choice options:x=-2x=-3y=6y=7y=11/2please show work!

Answer 1

Given the System of Equations:

`\begin{cases}y=x+7 \\ \\ y=(1)/(4)x+(11)/(2)\end{cases}`

You can apply the following steps in order to solve it using the Substitution Method:

1. Substitute the second equation into the first equation:

`(1)/(4)x+(11)/(2)=x+7`

2. Solve for "x":

`\begin{gathered} (1)/(4)x-x=7-(11)/(2) \\ \\ -(3)/(4)x=(3)/(2) \end{gathered}`

`\begin{gathered} x=((3)/(2))(-(4)/(3)) \\ \\ x=-(12)/(6) \\ \\ x=-2 \end{gathered}`

3. You can substitute the value of "x" into the first original equation:

`\begin{gathered} y=x+7 \\ y=(-2)+7 \end{gathered}`

4. Evaluating, you get this value of "y":

`\begin{gathered} y=-2+7 \\ y=5 \end{gathered}`

Hence, the answer is: First option.