Question

What is the x-value of the solution to the system of equations?

5x + 4y =8
2x- 3y = 17
O -3
O -2
O 4
O5

Answer 1

The solution to the system of equations is:

`x=4,\:y=-3`

Explanation:

Given the system of equations

`5x + 4y =8`

`2x- 3y = 17`

solving the system of equations

`\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}`

`\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16`

`\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85`

`\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}`

`10x-15y=85`

`-`

`\underline{10x+8y=16}`

`-23y=69`

`\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}`

solve for y

`-23y=69`

Divide both sides by -23

`(-23y)/(-23)=(69)/(-23)`

`y=-3`

`\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3`

`10x+8\left(-3\right)=16`

`10x-24=16`

`10x=40`

Divide both sides by 10

`(10x)/(10)=(40)/(10)`

`x=4`

Thus, the solution to the system of equations is:

`x=4,\:y=-3`