Answer:
The solution to the system is (1.8, 7.6)
Explanation:
To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.
Plot the lines:
y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.
y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.
Find the intersection point:
To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.
Substitute x from y = 2/3x + 4 into y = -x + 1:
-x + 1 = 2/3x + 4
Multiplying both sides by -3, we get:
3x - 3 = -2x - 12
Adding 2x to both sides, we get:
5x - 3 = -12
Adding 12 to both sides, we get:
5x = 9
Dividing both sides by 5, we get:
x = 1.8
Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:
y = 2/3x + 4
y = 2/3 * 1.8 + 4
y = 3.6 + 4
y = 7.6
So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.