Question

Use the image to answer the question.

A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4 . Find the solution to both equations.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution to both equations, we need to find the point where the two lines intersect on the graph.

For the equation x-5y=7, we can rearrange it to solve for x:
x = 5y + 7

For the equation 3x-2y=-4, we can rearrange it to solve for x:
3x = 2y -4
x = (2y - 4) / 3

Now we can set the two equations for x equal to each other and solve for y:
5y + 7 = (2y - 4) / 3
15y + 21 = 2y - 4
13y = -25
y = -25 / 13

Now that we have the value for y, we can substitute it back into one of the original equations to solve for x. Let's use x = 5y + 7 from the first equation:
x = 5(-25/13) + 7
x = -125/13 + 91/13
x = -34/13

Therefore, the solution to the system of equations x-5y=7 and 3x-2y=-4 is x = -34/13 and y = -25/13.

Answer 2

What is the intersection point?

Answer 3

[AI-generated answer — Bot GPT 3.5]

The intersection point is where the two lines intersect on the coordinate plane. In this case, the intersection point is at x = -34/13 and y = -25/13. This means that the two lines intersect at the coordinates (-34/13, -25/13), which falls in Quadrant 4 on the coordinate plane.