Question

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. (1 point) The intersection point is (?).

Answer 1

To find the solution to the system of equations, we can either solve for one variable in terms of the other and then substitute this into the other equation, or use elimination method.

Given equations are:
x - 5y = 7
3x - 2y = -4

Let's solve for x in terms of y from the first equation:
x = 5y + 7

Substitute x = 5y + 7 into the second equation:
3(5y + 7) - 2y = -4
15y + 21 - 2y = -4
13y + 21 = -4
13y = -25
y = -25/13

Now substitute y = -25/13 back into x = 5y + 7 to find x:
x = 5(-25/13) + 7
x = -125/13 + 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. The intersection point is (-34/13, -25/13).