Estimate the solution of the system of the linear equations based on the graph y = 2x + 3y = 1/2 x + 6
To estimate the solution of the system of linear equations y = 2x + 3 and y = 1/2x + 6 based on the graph, we need to find the point where the two lines intersect.
By looking at the equations, we can see that both equations are in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
For the equation y = 2x + 3, the slope is 2 and the y-intercept is 3.
For the equation y = 1/2x + 6, the slope is 1/2 and the y-intercept is 6.
To find the point of intersection, we can set the two equations equal to each other:
2x + 3 = 1/2x + 6
Solving for x:
2x - 1/2x = 6 - 3
(4/2)x - (1/2)x = 3
(3/2)x = 3
x = 3 / (3/2)
x = 3 * 2 / 3
x = 2
Now that we have found the x-coordinate, we can plug it back into either equation to find the y-coordinate:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the estimated solution to the system of equations y = 2x + 3 and y = 1/2x + 6 is (2, 7).