Answer:
The solution to the system of linear equations
[tex]y=4,\:x=2[/tex]
i.e. (x, y) = (2, 4)
The graph is also attached.
Step-by-step explanation:
Given the system of linear equations
[tex]y=3x-2[/tex]
[tex]y-2=x[/tex]
solving the system
[tex]\begin{bmatrix}y=3x-2\\ y-2=x\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-3x=-2\\ y-x=2\end{bmatrix}[/tex]
[tex]y-x=2[/tex]
[tex]-[/tex]
[tex]\underline{y-3x=-2}[/tex]
[tex]2x=4[/tex]
solve for x
[tex]2x=4[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{4}{2}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{For\:}y-3x=-2\mathrm{\:plug\:in\:}x=2[/tex]
[tex]y-3\cdot \:2=-2[/tex]
[tex]y-6=-2[/tex]
[tex]y=4[/tex]
Thus, the solution to the system of linear equations
[tex]y=4,\:x=2[/tex]
i.e. (x, y) = (2, 4)
The graph is also attached.
