Question

Solve the system of equations below using substitution.

x=3y−5


6x−2y=34


(1 point)
Responses

(112, 39)
(112, 39)

(4, 7)
(4, 7)

(-5, -32)
(-5, -32)

(7, 4)

Answer 1

To solve the system of equations using substitution, we'll follow these steps:

1. The equations are:
\[
x = 3y - 5 \quad (1)
\]
\[
6x - 2y = 34 \quad (2)
\]

2. Substitute the expression for \(x\) from equation (1) into equation (2):
\[
6(3y - 5) - 2y = 34
\]

3. Distributing the 6:
\[
18y - 30 - 2y = 34
\]

4. Combine like terms:
\[
16y - 30 = 34
\]

5. Add 30 to both sides:
\[
16y = 64
\]

6. Divide by 16 to solve for \(y\):
\[
y = 4
\]

7. Now substitute \(y = 4\) back into equation (1) to find \(x\):
\[
x = 3(4) - 5 = 12 - 5 = 7
\]

So, the solution to the system of equations is:
\[
(x, y) = (7, 4)
\]

Therefore, the correct answer is:
**(7, 4)**