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

y=-2x+3
y=5x-4
A. (-1,-1)
B. (1,-1)
C. (-1,1)
D. (1,1)

1 answer

To estimate the solution to the system of linear equations based on the graph, we need to find the point of intersection of the two lines.

The given equations are:
y = -2x + 3 ...(1)
y = 5x - 4 ...(2)

To find the point of intersection, we need to equate the y-values in both equations.

-2x + 3 = 5x - 4

Bringing all the x-terms to one side and all the constant terms to the other side, we get:

-2x - 5x = -4 - 3
-7x = -7

Dividing both sides by -7, we get:
x = 1

Substituting the value of x = 1 into equation (1), we can find the value of y:

y = -2(1) + 3
y = -2 + 3
y = 1

Therefore, the estimated solution to the system of linear equations based on the graph is (1, 1).

So, the correct option is: D. (1, 1)