Solving Equations Using Substitution Quick Check

Question

4 of 54 of 5 Items

Question
Solve the system of equations.
−4x+6y=38
x−5y=−20(1 point)
Responses

(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis

(5, 3)
left parenthesis 5 comma 3 right parenthesis

(−35, −3)
left parenthesis negative 35 comma negative 3 right parenthesis

(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
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Answer 1

To solve the system of equations using substitution, we can start by isolating one of the variables in the second equation. Let's isolate x:

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

Now we can substitute x with 5y - 20 in the first equation:

-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 x = 5y - 20:

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

Therefore, the solution to the system of equations is (-5, 3). So the correct response is:
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis