Question

systems of equations - substitution
a system of equations is shown below.
\

$$\begin{cases}5x + 8y = 0\\\\y = 0.5x - 9\\end{cases}$$

what is the value of x in the solution to the system of equations?
x = \square

Explanation:

Step1: Substitute \( y \) into first equation

We know \( y = 0.5x - 9 \), substitute into \( 5x + 8y = 0 \).
So \( 5x + 8(0.5x - 9) = 0 \).

Step2: Simplify and solve for \( x \)

Expand the equation: \( 5x + 4x - 72 = 0 \).
Combine like terms: \( 9x - 72 = 0 \).
Add 72 to both sides: \( 9x = 72 \).
Divide by 9: \( x = \frac{72}{9} = 8 \).

Answer:

\( x = 8 \)