Answer:
The solution to the system of equation
[tex]y=10,\:x=-5[/tex]
Step-by-step explanation:
Given the system of equation
[tex]\begin{bmatrix}y+3x=-5\\ y-4x=30\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y+3x=-5\\ y-4x=30\end{bmatrix}[/tex]
subtracting the equation
[tex]y-4x=30[/tex]
[tex]-[/tex]
[tex]\underline{y+3x=-5}[/tex]
[tex]-7x=35[/tex]
[tex]\begin{bmatrix}y+3x=-5\\ -7x=35\end{bmatrix}[/tex]
solve -7x = 35 for x
[tex]-7x=35[/tex]
divide both sides by -7
[tex]\frac{-7x}{-7}=\frac{35}{-7}[/tex]
[tex]x=-5[/tex]
For y + 3x = -5 plug in x = -5
[tex]y+3\left(-5\right)=-5[/tex]
[tex]y-15=-5[/tex]
Add 15 to both sides
[tex]y-15+15=-5+15[/tex]
Simplify
[tex]y=10[/tex]
Therefore, the solution to the system of equation
[tex]y=10,\:x=-5[/tex]
