Answer:
The solution to the system of equations is:
[tex]x=4,\:y=-3[/tex]
Step-by-step explanation:
Given the system of equations
[tex]5x + 4y =8[/tex]
[tex]2x- 3y = 17[/tex]
solving the system of equations
[tex]\begin{bmatrix}5x+4y=8\\ 2x-3y=17\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}5x+4y=8\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:10x+8y=16[/tex]
[tex]\mathrm{Multiply\:}2x-3y=17\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:10x-15y=85[/tex]
[tex]\begin{bmatrix}10x+8y=16\\ 10x-15y=85\end{bmatrix}[/tex]
[tex]10x-15y=85[/tex]
[tex]-[/tex]
[tex]\underline{10x+8y=16}[/tex]
[tex]-23y=69[/tex]
[tex]\begin{bmatrix}10x+8y=16\\ -23y=69\end{bmatrix}[/tex]
solve for y
[tex]-23y=69[/tex]
Divide both sides by -23
[tex]\frac{-23y}{-23}=\frac{69}{-23}[/tex]
[tex]y=-3[/tex]
[tex]\mathrm{For\:}10x+8y=16\mathrm{\:plug\:in\:}y=-3[/tex]
[tex]10x+8\left(-3\right)=16[/tex]
[tex]10x-24=16[/tex]
[tex]10x=40[/tex]
Divide both sides by 10
[tex]\frac{10x}{10}=\frac{40}{10}[/tex]
[tex]x=4[/tex]
Thus, the solution to the system of equations is:
[tex]x=4,\:y=-3[/tex]
