Question

Solve the system of two equations using substitution.
−4x+6y=38
x−5y=−20

Answer 1

First, solve one of the equations for one variable in terms of the other variable. Let's use the second equation, x - 5y = -20, to solve for x:

x = 5y - 20

Next, substitute this expression for x into the first equation, -4x + 6y = 38:

-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y + 80 = 38
-14y = -42
y = 3

Now that we have found the value of y, we can substitute it back into the equation x = 5y - 20 to solve for x:

x = 5(3) - 20
x = 15 - 20
x = -5

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