Solve the system of equations

Question

-4x+6y=38
x-5y=-20

Answer 1

To solve the system of equations, we can either use the substitution method or the elimination method.

Using the substitution method:
From the second equation, we can isolate x:
x - 5y = -20
x = 5y - 20

Now, substitute x in the first equation with its value:
-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y = -42
y = -42 / -14
y = 3

Substitute y back into the second equation to find x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.

Using the elimination method:
Multiply the second equation by 4 to make the coefficients of x in both equations the same:
4(x - 5y) = 4(-20)
4x - 20y = -80

Now, add this equation to the first equation:
-4x + 6y + 4x - 20y = 38 - 80
-14y = -42
y = -42 / -14
y = 3

Substitute y back into the second equation to find x:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.