Question

x 3x + y = 3 x + y = 2 Solve the system of equations. A x = 1/2 y = 3 B x = 3 y = 1/2 x = 1/2 y = 3/2 Dx x = 3/2 y = 1/2 x = 5/2 y = - 9/2

Answer 1

To solve the system of equations given:

1. \( 3x + y = 3 \) (Equation 1)
2. \( x + y = 2 \) (Equation 2)

We can use substitution or elimination. Here, we will use substitution.

From Equation 2, we can express \(y\) in terms of \(x\):

\[
y = 2 - x
\]

Now, substitute \(y\) in Equation 1:

\[
3x + (2 - x) = 3
\]

Simplifying:

\[
3x + 2 - x = 3
\]
\[
2x + 2 = 3
\]
\[
2x = 1
\]
\[
x = \frac{1}{2}
\]

Next, we substitute \(x = \frac{1}{2}\) back into the equation for \(y\):

\[
y = 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}
\]

Thus, the solution to the system of equations is:

\[
x = \frac{1}{2}, \quad y = \frac{3}{2}
\]

This solution corresponds to option (A):

**A** \(x = \frac{1}{2}, y = \frac{3}{2}\)