Question

what is the x - value of the solution to the system of equations?
$5x + 4y = 8$
$2x - 3y = 17$
○ $-3$
○ $-2$
○ $4$
○ $5$

Explanation:

Step1: Eliminate y by scaling equations

Multiply the first equation \(5x + 4y = 8\) by 3: \(15x + 12y = 24\).
Multiply the second equation \(2x - 3y = 17\) by 4: \(8x - 12y = 68\).

Step2: Add the scaled equations

Add \(15x + 12y = 24\) and \(8x - 12y = 68\):
\(15x + 8x + 12y - 12y = 24 + 68\)
\(23x = 92\).

Step3: Solve for x

Divide both sides by 23: \(x = \frac{92}{23} = 4\).

Answer:

4 (corresponding to the option "4")