An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals 3 x minus 2. The equation of the dotted line is y equals negative x plus 6. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.

Question

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

y=−x+6


y=3x−2


(1 point)
(
,
)

Answer 1

To find the solution to the system of linear equations represented by the lines \( y = -x + 6 \) and \( y = 3x - 2 \), we can set the two equations equal to each other to find the intersection point.

1. Set the equations equal to each other:

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

2. Rearranging gives:

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

\[ 8 = 4x \]

3. Solving for \( x \):

\[ x = \frac{8}{4} = 2 \]

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

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

Thus, the intersection (solution) of the system of equations is:

\[ (2, 4) \]

So the estimated solution to the system of these linear equations based on the graph is (2, 4).