Question

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

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, I will use the substitution method.

First, solve Equation 1 for \( y \):

\[
y = 2 - 3x
\]

Next, substitute \( y \) in Equation 2:

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

Distributing \( -4 \):

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

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 expression for \( y \):

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

So the solution to the system of equations is:

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

Thus, the correct choice is:

• (2, -4)