Question

Consider the following system of equations:2x+3y=45x+y=10What is the x-value of the solution for this system?(1 point)

Answer 1

To solve the system of equations:

1. \( 2x + 3y = 4 \) (Equation 1)
2. \( 5x + y = 10 \) (Equation 2)

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

First, let's solve Equation 2 for \( y \):

\[
y = 10 - 5x
\]

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

\[
2x + 3(10 - 5x) = 4
\]

Now, distribute the \( 3 \):

\[
2x + 30 - 15x = 4
\]

Combine like terms:

\[
-13x + 30 = 4
\]

Now, isolate \( x \):

\[
-13x = 4 - 30
\]
\[
-13x = -26
\]

Now, divide both sides by -13:

\[
x = 2
\]

Thus, the x-value of the solution for this system is \( \boxed{2} \).