Question

solve the system of equations by graphing -x + 2y = 5 and 2x - 4y = -8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations by graphing -x + 2y = 5 and 2x - 4y = -8, we first need to rewrite the equations in slope-intercept form (y = mx + b).

Equation 1: -x + 2y = 5
2y = x + 5
y = 1/2x + 5/2

Equation 2: 2x - 4y = -8
-4y = -2x - 8
y = 1/2x + 2

Now we can graph both equations on the same coordinate system:

Equation 1 (y = 1/2x + 5/2):
- Plot the y-intercept at (0, 5/2)
- Use the slope of 1/2 to plot another point: move up 1 unit and right 2 units from the y-intercept to the point (2, 3)

Equation 2 (y = 1/2x + 2):
- Plot the y-intercept at (0, 2)
- Use the slope of 1/2 to plot another point: move up 1 unit and right 2 units from the y-intercept to the point (2, 3)

Now draw a line through both points for each equation. The point at which the two lines intersect is the solution to the system of equations.

The lines intersect at the point (2, 3), so the solution to the system is x = 2 and y = 3.

Therefore, the system of equations -x + 2y = 5 and 2x - 4y = -8 is solved by graphing at x = 2 and y = 3.