Question

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

5x + 4y = 8

2x − 3y = 17

−3
−2
4
5

Answer 1

To solve the system of equations, we'll use the method of substitution or elimination. Let's consider the system:

1. \( 5x + 4y = 8 \) (Equation 1)
2. \( 2x - 3y = 17 \) (Equation 2)

We can solve one of the equations for \( y \) and substitute into the other. Let's solve Equation 1 for \( y \):

\[
4y = 8 - 5x
\]
\[
y = \frac{8 - 5x}{4}
\]

Now we can substitute this expression for \( y \) into Equation 2:

\[
2x - 3\left(\frac{8 - 5x}{4}\right) = 17
\]

Now we'll simplify this equation:

\[
2x - \frac{3(8 - 5x)}{4} = 17
\]
Multiply every term by 4 to eliminate the fraction:

\[
4(2x) - 3(8 - 5x) = 4(17)
\]
\[
8x - 24 + 15x = 68
\]
Combine the \( x \) terms:

\[
23x - 24 = 68
\]
Add 24 to both sides:

\[
23x = 92
\]
Now divide by 23:

\[
x = \frac{92}{23} = 4
\]

Thus, the x-value of the solution to the system of equations is **4**.