Solve the system of equations.

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)