solve the system by graphing "-x+4y=-2" "-2x+5y=-4"

Answer 1

To graph the system of equations, first convert each equation into slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept. Then plot the lines on a graph and find their intersection point, which represents the solution to the system.

1) -x + 4y = -2
Add x to both sides:
4y = x - 2
Divide by 4:
y = (1/4)x - 1/2

2) -2x + 5y = -4
Add 2x to both sides:
5y = 2x - 4
Divide by 5:
y = (2/5)x - 4/5

Now we can graph the equations:

Graph 1: y = (1/4)x - 1/2
Plot the y-intercept at -1/2 (0, -1/2) and use the slope to find additional points. For example, when x = 4, y = (1/4)(4) - 1/2 = 1 - 1/2 = 1/2, giving us the point (4, 1/2).

Graph 2: y = (2/5)x - 4/5
Plot the y-intercept at -4/5 (0, -4/5) and use the slope to find additional points. For example, when x = 5, y = (2/5)(5) - 4/5 = 2 - 4/5 = 6/5, so we get the point (5, 6/5).

Now we can plot these points on a graph:

{{{ graph( 300, 200, -5, 5, -5, 5, (1/4)x - 1/2, (2/5)x - 4/5) }}}

The solution to the system is the intersection point of the two lines. From the graph, it appears to be approximately (2, -1/4).