1. 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.

Question

On a graph there's 3x - 2y = -4 and x - 5y = 3.

The intersection point is (____).

Answer 1

To find the solution to both equations, we can set them equal to each other and solve for x and y:

x - 5y = 7
3x - 2y = -4

From the second equation, we can solve for x in terms of y:

3x - 2y = -4
3x = 2y - 4
x = (2y - 4)/3

Now, we can substitute this expression for x into the first equation and solve for y:

(2y - 4)/3 - 5y = 7
2y - 4 - 15y = 21
-13y = 25
y = -25/13

Now that we have found the value of y, we can substitute it back into the expression for x to find its value:

x = (2(-25/13) - 4)/3
x = (-50/13 - 52/13)/3
x = (-102/13)/3
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. The intersection point is (-34/13, -25/13).