Question

Solving Equations Using Substitution Quick Check
3 of 53 of 5 Items




Question
Solve the system of equations.
3x+y=2

7x−4y=30
(1 point)
Responses

(2, −2)
left parenthesis 2 comma negative 2 right parenthesis

(2, −4)
left parenthesis 2 comma negative 4 right parenthesis

(−2, 8)
left parenthesis negative 2 comma 8 right parenthesis

(12, 12)

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. \(3x + y = 2\) (Equation 1)
2. \(7x - 4y = 30\) (Equation 2)

Let's solve Equation 1 for \(y\):

\[
y = 2 - 3x
\]

Now we can substitute this expression for \(y\) into Equation 2:

\[
7x - 4(2 - 3x) = 30
\]

Distributing the \(-4\):

\[
7x - 8 + 12x = 30
\]

Combining like terms:

\[
19x - 8 = 30
\]

Adding \(8\) to both sides:

\[
19x = 38
\]

Dividing both sides by \(19\):

\[
x = 2
\]

Now we substitute \(x = 2\) back into the expression for \(y\):

\[
y = 2 - 3(2) = 2 - 6 = -4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (2, -4)
\]

So the correct response is:

**(2, −4)**