Question

Solve the system of equations.
3х + y=2
7x - 4y = 30 (1 point)
O (-2,8)
O (2, - 2)
O (2, - 4)

Answer 1

To solve the system of equations provided:

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

We can solve this system of equations using substitution or elimination. Let's use substitution in this case.

### Step 1: Solve for \(y\) in Equation 1

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

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

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

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

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

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

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

Divide by 19:
\[
x = 2
\]

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

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

### Solution

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

### Final Answer

Among the given options, the correct solution is:
**O (2, -4)**