Solve the system of equations by graphing.
\[
\begin{array}{l}
4 x-y=6 \\
x+2 y=6
\end{array}
\]

Select the correct choice and, If necessary, fill in the answer box to complefe your choice.
A. The solution is $\square$.
(T), an ordered paic)
B. There are intinitely many solvitions.
c. There is no sclution.

Answer

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Answer

$\boxed{(2, 2)}$ is the solution to the system of equations.

Steps

Step 1 ：Rewrite the first equation, $4x - y = 6$, in slope-intercept form to get $y = 4x - 6$.

Step 2 ：Rewrite the second equation, $x + 2y = 6$, in slope-intercept form to get $y = -\frac{1}{2}x + 3$.

Step 3 ：Graph the two equations $y = 4x - 6$ and $y = -\frac{1}{2}x + 3$ on the same set of axes.

Step 4 ：Find the point where the two lines intersect. This point is the solution to the system of equations.

Step 5 ：The lines intersect at the point $(2, 2)$.

Step 6 ：$\boxed{(2, 2)}$ is the solution to the system of equations.