Answer:
The solution to the system of equations is:
[tex]x=5,\:y=3[/tex]
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x+2y=11\\ y=x-2\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}x+2y=11\\ -x+y=-2\end{bmatrix}[/tex]
adding
[tex]-x+y=-2[/tex]
[tex]+[/tex]
[tex]\underline{x+2y=11}[/tex]
[tex]3y=9[/tex]
so
[tex]\begin{bmatrix}x+2y=11\\ 3y=9\end{bmatrix}[/tex]
solving for y
[tex]3y=9[/tex]
Divide both sides by 3
[tex]\frac{3y}{3}=\frac{9}{3}[/tex]
[tex]y=3[/tex]
[tex]\mathrm{For\:}x+2y=11\mathrm{\:plug\:in\:}y=3[/tex]
[tex]x+2\cdot \:3=11[/tex]
[tex]x+6=11[/tex]
[tex]x=5[/tex]
Thus, the solution to the system of equations is:
[tex]x=5,\:y=3[/tex]
