Question

Review the graph of a system of two liner equations in two variables: x -5y = 7 and 3x - 2y = -4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the system of equations x - 5y = 7 and 3x - 2y = -4, we can rearrange each equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

For the first equation x - 5y = 7:
-5y = -x + 7
y = (1/5)x - 7/5

For the second equation 3x - 2y = -4:
-2y = -3x - 4
y = (3/2)x + 2

Now we can plot these two lines on a graph:

For y = (1/5)x - 7/5, we start at the y-intercept of -7/5 and move up 1 unit and right 5 units to find another point. We can draw a straight line through these two points.

For y = (3/2)x + 2, we start at the y-intercept of 2 and move up 3 units and right 2 units to find another point. We can draw a straight line through these two points.

The two lines intersect at the point (-3,-2), which is the solution to the system of equations x - 5y = 7 and 3x - 2y = -4. This point is the solution because it satisfies both equations at the same time.