Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

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).

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations by graphing, we will plot the lines represented by each equation and find the point of intersection, which represents the solution.

Let's start with the first equation:

-x + 4y = -2

To graph this equation, we should rearrange it in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

4y = x - 2
y = (1/4)x - 1/2

Now let's graph the second equation:

-2x + 5y = -4

Again, rearrange it in the slope-intercept form:

5y = 2x - 4
y = (2/5)x - (4/5)

Now, plot the two lines on a graph:

Graph of y = (1/4)x - 1/2:
- Plot the point (0, -1/2) as the y-intercept.
- Then, move up 1 unit and right 4 units to find another point.
- Connect the two points with a straight line.

Graph of y = (2/5)x - (4/5):
- Plot the point (0, -4/5) as the y-intercept.
- Move up 2 units and right 5 units to find another point.
- Connect the two points with a straight line.

Now, observe the graph and find the point of intersection:
The two lines intersect at the point (4, 1).

So, the solution to the system of equations is x = 4 and y = 1.