Estimate the solution to the system of these linear equations based on the graph
y = 2x + 3
y = 1/2x + 6
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.
To estimate the solution to the system of linear equations, we can look at the intersection point of the two graphs.
First, let's rewrite the equations in slope-intercept form:
Equation 1: y = 2x + 3
Equation 2: y = (1/2)x + 6
Now, we can see that the slopes of the two lines are different. The slope of the first line is 2 while the slope of the second line is 1/2. This means that the lines are not parallel and will intersect at a single point.
To find this point of intersection, we can set the two equations equal to each other:
2x + 3 = (1/2)x + 6
Next, we can solve this equation for x:
2x - (1/2)x = 6 - 3
(4/2)x - (1/2)x = 3
(3/2)x = 3
x = 3 * (2/3)
x = 2
Now that we have the x-coordinate (x = 2), we can substitute it into either equation to find the corresponding y-coordinate. Let's use Equation 1:
y = 2(2) + 3
y = 4 + 3
y = 7
Therefore, the estimated solution to the system of linear equations (based on the graph) is (2, 7).