Question

Solve the system of equations.

4x + y = 2
x − y = 3

Group of answer choices

x = 1

x = 0

x = -5

x = 4

Answer 1

To solve the system of equations:

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

We can use substitution or elimination. I'll solve it using substitution.

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

\[
y = x - 3
\]

Now, we can substitute this expression for \( y \) into Equation 1:

\[
4x + (x - 3) = 2
\]

Combine the terms:

\[
4x + x - 3 = 2
\]
\[
5x - 3 = 2
\]

Now, add 3 to both sides:

\[
5x = 5
\]

Now, divide by 5:

\[
x = 1
\]

Now we substitute \( x = 1 \) back into the expression we found for \( y \):

\[
y = 1 - 3 = -2
\]

So, the solution to the system of equations is:

\[
x = 1, \quad y = -2
\]

Thus, from the given options for \( x \):
- The correct answer is \( x = 1 \).