Question

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

7x−4y=30

Answer 1

To solve the system of equations:

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

We can substitute Equation 1 into Equation 2 after expressing \( y \) in terms of \( x \) from Equation 1.

From Equation 1, we can solve for \( y \):

\[
y = 2 - 3x
\]

Next, we substitute this expression for \( y \) into Equation 2:

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

Now, let's simplify this equation:

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

Combine like terms:

\[
19x - 8 = 30
\]

Now, add 8 to both sides:

\[
19x = 38
\]

Divide both sides by 19:

\[
x = 2
\]

Now that we have \( x \), we can substitute back to find \( y \):

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

Thus, the solution to the system of equations is:

\[
\boxed{(2, -4)}
\]