Question

What is the x-value in the solution to this system of linear equations?

2x − y = 11

x + 3y = −5

−3
−1
2
4

Answer 1

To solve the system of linear equations and find the x-value, we can use either substitution or elimination. Here, I'll use the elimination method.

The equations are:

1. \( 2x - y = 11 \) (Equation 1)
2. \( x + 3y = -5 \) (Equation 2)

First, we'll manipulate one of the equations to eliminate \( y \). Let's express \( y \) in terms of \( x \) from Equation 1:

From Equation 1:
\[
y = 2x - 11
\]

Now, substitute \( y \) into Equation 2:

\[
x + 3(2x - 11) = -5
\]

Distributing \( 3 \):
\[
x + 6x - 33 = -5
\]
Combine like terms:
\[
7x - 33 = -5
\]

Now, add \( 33 \) to both sides:
\[
7x = 28
\]

Next, divide by \( 7 \):
\[
x = 4
\]

Thus, the x-value in the solution to this system of linear equations is \( \boxed{4} \).