Question

solve the system of equations by graphing -x + 2y = 5 and 2x - 4y = -8
i think the answer is (3, 2)

Answer 1

To solve the system of equations by graphing, we need to graph the two equations and find the point of intersection.

First, let's graph the equation -x + 2y = 5.
To graph this equation, we'll find the x and y-intercepts:
1. When x = 0:
-0 + 2y = 5
2y = 5
y = 2.5 (or 5/2)
So, the y-intercept is at (0, 2.5).

2. When y = 0:
-x + 2(0) = 5
-x = 5
x = -5
So, the x-intercept is at (-5, 0).

Now, we plot these two points and draw a line through them.

Next, let's graph the equation 2x - 4y = -8.
Again, we'll find the x and y-intercepts:
1. When x = 0:
2(0) - 4y = -8
-4y = -8
y = 2
So, the y-intercept is at (0, 2).

2. When y = 0:
2x - 4(0) = -8
2x = -8
x = -4
So, the x-intercept is at (-4, 0).

Now, we plot these two points and draw a line through them.

The point of intersection of the two lines is (3, 2). Therefore, the solution to the system of equations is x = 3 and y = 2.