Answer:
The solution to the system of equations be:
[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]
Step-by-step explanation:
Given the system of equation
[tex]\begin{bmatrix}-x+5y=8\\ 3x+7y=-3\end{bmatrix}[/tex]
Multiply -x+5y=8 by 3: -3x+15y=24
[tex]\begin{bmatrix}-3x+15y=24\\ 3x+7y=-3\end{bmatrix}[/tex]
Add the equations
[tex]3x+7y=-3[/tex]
[tex]+[/tex]
[tex]\underline{-3x+15y=24}[/tex]
[tex]22y=21[/tex]
solving 22y=21 for y
[tex]22y=21[/tex]
Divide both sides by 22
[tex]\frac{22y}{22}=\frac{21}{22}[/tex]
Simplify
[tex]y=\frac{21}{22}[/tex]
For -3x+15y=24 plug in y = 21/22
[tex]-3x+15\cdot \frac{21}{22}=24[/tex]
Subtract 15 · 21/22 from both sides
[tex]-3x+15\cdot \frac{21}{22}-15\cdot \frac{21}{22}=24-15\cdot \frac{21}{22}[/tex]
[tex]-3x=\frac{213}{22}[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}=\frac{\frac{213}{22}}{-3}[/tex]
[tex]x=-\frac{71}{22}[/tex]
The solution to the system of equations be:
[tex]x=-\frac{71}{22},\:y=\frac{21}{22}[/tex]
