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

y = 2x + 3
y = 1/2x + 6

1 answer

Based on the graph, it appears that the two lines intersect at a point. This point represents the solution to the system of linear equations.

Therefore, we can estimate the solution to be the coordinates of the point of intersection.

From the equations y = 2x + 3 and y = (1/2)x + 6, we can set them equal to each other to solve for x:

2x + 3 = (1/2)x + 6

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:

4x + 6 = x + 12

Subtracting x from both sides and subtracting 6 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

Plugging x = 2 into either equation, we can solve for y:

y = 2(2) + 3 = 4 + 3 = 7

Therefore, the estimated solution to the system of linear equations is x = 2 and y = 7.