solve the system of equations.

Question

-2x-5y=-5
x-5y=-20

A. (-5,3)
B.(5,3)
C.(-5,-3)
D.(3,5)

Answer 1

To solve this system of equations, we can use the elimination method.

First, let's multiply the second equation by -2:
-2(x-5y) = -2(-20)
-2x + 10y = 40

Now we have the system of equations:
-2x - 5y = -5
-2x + 10y = 40

Adding the two equations together:
-2x - 5y + (-2x + 10y) = -5 + 40
-2x - 2x + 5y + 10y = 35
-4x + 15y = 35

Now we can isolate one variable by solving this equation for x or y:
-4x + 15y = 35
4x = 15y - 35
x = (15y - 35)/4

Now we can substitute this expression for x into one of the original equations, for example:
x - 5y = -20
(15y - 35)/4 - 5y = -20
15y - 35 - 20y = -80
-5y - 35 = -80
-5y = -45
y = 9

Now that we have found the value of y, we can substitute it back into the expression for x:
x = (15(9) - 35)/4
x = (135 - 35)/4
x = 100/4
x = 25

Therefore, the solution to the system of equations is x = 25 and y = 9, which corresponds to option B, (25, 9).