An illustration of a coordinate plane with four quadrants shows a solid line and a dotted line with arrows at both the ends intersecting with each other. The x axis extends from negative 10 to 10 in increments of 1. The y axis extends from negative 5 to 15 in increments of 1. The equation of the solid line is y equals negative 2 x plus 10. The equation of the dotted line is y equals negative 5 x plus 7. The lines intersect at left parenthesis negative 1 comma 12 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=−5x+7

y=−2x+10
(1 point)
Responses

(−1,−12)
left parenthesis negative 1 comma negative 12 right parenthesis

(12,−1)
left parenthesis 12 comma negative 1 right parenthesis

(1,−12)
left parenthesis 1 comma negative 12 right parenthesis

(−1, 12)

Answer 1

To estimate the solution to the system of linear equations given by:

1. \( y = -5x + 7 \) (dotted line)
2. \( y = -2x + 10 \) (solid line)

and noting that the lines intersect at the point \((-1, 12)\), we can conclude that the solution to the system of equations is:

\[ \boxed{(-1, 12)} \]

This point represents the values of \(x\) and \(y\) where the two lines intersect on the coordinate plane.