Solving Equations Using Substitution Quick Check

Question

3 of 53 of 5 Items

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

7x−4y=30
(1 point)
Responses

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

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

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

(12, 12)

Answer 1

To solve the system of equations using substitution, we start with the two equations:

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

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

\[ y = 2 - 3x \]

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

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

Distributing the \(-4\):

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

Combine like terms:

\[ (7x + 12x) - 8 = 30 \] \[ 19x - 8 = 30 \]

Add 8 to both sides:

\[ 19x = 38 \]

Divide by 19:

\[ x = 2 \]

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

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

So the solution to the system of equations is:

(2, -4)

Thus, the correct response is:

(2, −4).