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