Question

solve the system of equations

3x + y = 2
7x - 4y = 30

(1/2, 1/2)
(2, -2)
(-2, 8)
(2, -4)

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. Let's use substitution here.

From the first equation, we can solve for \(y\):

\[
y = 2 - 3x
\]

Now, we substitute this expression for \(y\) into the second equation:

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

Now, distribute the \(-4\):

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

Combine like terms:

\[
19x - 8 = 30
\]

Add \(8\) to both sides:

\[
19x = 38
\]

Now, divide by \(19\):

\[
x = 2
\]

Now, substitute \(x = 2\) back into the equation for \(y\):

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

So, the solution to the system of equations is:

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

Now, let's verify it with the given options:

- \((1/2, 1/2)\)
- \((2, -2)\)
- \((-2, 8)\)
- \((2, -4)\)

The correct answer is \((2, -4)\).