Estimate the solution to the system of these linear equations based on the graph. Y equals 2x + 3 and y equals 1/2x + 6, out of the following options, which is the correct? (2, 7), (2, -7), (7, 2) or (-2, 7)
To estimate the solution to the system of linear equations, we need to find the coordinates where the two lines intersect on the graph.
By comparing the two equations, we can see that both have y-intercepts of different values. The y-intercept of the equation y = 2x + 3 is 3, while the y-intercept of the equation y = 1/2x + 6 is 6.
When two lines intersect, their y-values must be equal. So, we can set the right sides of the equations equal to each other and solve for x:
2x + 3 = 1/2x + 6
Multiplying through by 2 to eliminate the fraction:
4x + 6 = x + 12
Simplifying the equation:
3x = 6
x = 2
Now that we have the value of x, we can substitute it into either of the original equations to find the corresponding value of y. Using y = 2x + 3:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the estimated solution to the system of linear equations is (2, 7).