Question

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

7x−4y=30
(1 point)
Responses

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

(12, 12)
left parenthesis start fraction 1 over 2 end fraction comma start fraction 1 over 2 end fraction right parenthesis

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

(2, −2)

Answer 1

To solve the system of equations, we will use the following two equations:

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

### Step 1: Solve for \(y\) in terms of \(x\) using Equation 1

From Equation 1:
\[
y = 2 - 3x
\]

### Step 2: Substitute \(y\) in Equation 2

Now substitute \(y\) into Equation 2:
\[
7x - 4(2 - 3x) = 30
\]

### Step 3: Simplify and solve for \(x\)

Distributing \( -4 \):
\[
7x - 8 + 12x = 30
\]

Combine like terms:
\[
19x - 8 = 30
\]

Add 8 to both sides:
\[
19x = 30 + 8
\]
\[
19x = 38
\]

Divide by 19:
\[
x = 2
\]

### Step 4: Substitute \(x\) back to find \(y\)

Now substitute \(x = 2\) back into the equation for \(y\):
\[
y = 2 - 3(2)
\]
\[
y = 2 - 6
\]
\[
y = -4
\]

### Solution

The solution to the system of equations is:
\[
(x, y) = (2, -4)
\]

### Conclusion

The correct answer from the options given is:
\((2, -4)\)