Question

Estimate the solution to the system of these linear equations based on the graph.

y=−x+6

y=3x−2

(2 points)
(
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Answer 1

To estimate the solution to the system of equations given by the lines \(y = -x + 6\) and \(y = 3x - 2\), let's find the intersection point of the two lines.

1. Set the equations equal to each other:

\[
-x + 6 = 3x - 2
\]

2. Solve for \(x\):

\[
6 + 2 = 3x + x
\]
\[
8 = 4x
\]
\[
x = 2
\]

3. Substitute \(x = 2\) back into one of the equations to find \(y\). Using \(y = -x + 6\):

\[
y = -2 + 6 = 4
\]

So, the intersection point, or the solution to the system of equations, is:

\[
(2, 4)
\]

Thus, the estimated solution to the system is \((2, 4)\).