Use the image to answer the question.

Question

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.

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 equations given by the lines:

1. \( y = -x + 6 \) (dotted line)
2. \( y = 3x - 2 \) (solid line)

we need to determine the point where these two lines intersect. According to your description, the intersection point of the two lines is given as \( (2, 4) \).

To confirm that \( (2, 4) \) is indeed the solution:

1. Substitute \( x = 2 \) into the first equation: \[ y = -2 + 6 = 4 \]
2. Substitute \( x = 2 \) into the second equation: \[ y = 3(2) - 2 = 6 - 2 = 4 \]

Since both equations yield \( y = 4 \) when \( x = 2 \), the point \( (2, 4) \) is indeed the solution to the system of equations.

Therefore, the estimated solution to the system of these linear equations is (2, 4).