Answer:
The solution to the system of equations be:
[tex]y=-3,\:x=2[/tex]
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}[/tex]
Let us solve the system by the elimination method
[tex]\begin{bmatrix}y=3x-9\\ y=-2x+1\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-3x=-9\\ y+2x=1\end{bmatrix}[/tex]
subtracting the equations
[tex]y+2x=1[/tex]
[tex]-[/tex]
[tex]\underline{y-3x=-9}[/tex]
[tex]5x=10[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}y-3x=-9\\ 5x=10\end{bmatrix}[/tex]
solve 5x for x
[tex]5x=10[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}=\frac{10}{5}[/tex]
[tex]x = 2[/tex]
[tex]\mathrm{For\:}y-3x=-9\mathrm{\:plug\:in\:}x=2[/tex]
[tex]y-3\cdot \:2=-9[/tex]
[tex]y-6=-9[/tex]
Add 6 to both sides
[tex]y-6+6=-9+6[/tex]
[tex]y=-3[/tex]
Therefore, the solution to the system of equations be:
[tex]y=-3,\:x=2[/tex]
