estimate the solution to the system of these linear equations based on the graph.
y = 2x + 3
y = 1/2x + 6
(7, 2)
(2, 7)
(2, -7)
(-2, 7)
Based on the graph, the estimated solution to the system of linear equations is (2, -7).
To estimate the solution to the system of linear equations based on the graph, we can observe where the two lines intersect.
The first equation is y = 2x + 3, which has a positive slope, indicating a line that slants upward. The y-intercept is 3, so the line crosses the y-axis at (0, 3).
The second equation is y = (1/2)x + 6, which has a smaller positive slope, indicating a less steep upward slant. The y-intercept is 6, so the line crosses the y-axis at (0, 6).
To estimate the solution, we can look at the given points, (7, 2), (2, 7), (2, -7), and (-2, 7), and check which point lies on both lines.
Let's plug in the x and y values of each point into both equations to see if they satisfy both equations:
For (7, 2):
Equation 1: 2(7) + 3 = 17
Equation 2: (1/2)(7) + 6 = 9.5
This point does not satisfy both equations because the y-value of Equation 1 and Equation 2 are different.
For (2, 7):
Equation 1: 2(2) + 3 = 7
Equation 2: (1/2)(2) + 6 = 7
This point satisfies both equations because the y-values of Equation 1 and Equation 2 are the same. So (2, 7) is a candidate for the solution.
For (2, -7):
Equation 1: 2(2) + 3 = 7
Equation 2: (1/2)(2) + 6 = 7
This point also satisfies both equations. So (2, -7) is another candidate for the solution.
For (-2, 7):
Equation 1: 2(-2) + 3 = -1
Equation 2: (1/2)(-2) + 6 = 5
This point does not satisfy both equations because the y-value of Equation 1 and Equation 2 are different.
Based on the graph, the lines intersect at (2, 7). So we can estimate that the solution to the system of linear equations is x = 2 and y = 7.