Question

what is the solution to the system of equations?
3x - 4y = 18
2x + 3y = 5
○ (-4, 1)
○ (4, -1)
○ (-4, -1)
○ (4, 1)

Explanation:

Step1: Eliminate x variable

Multiply first eq by 2, second by 3:
$2(3x-4y)=2(18) \implies 6x-8y=36$
$3(2x+3y)=3(5) \implies 6x+9y=15$

Step2: Subtract equations

Subtract new first from new second:
$(6x+9y)-(6x-8y)=15-36$
$17y=-21$

Step3: Solve for y

Calculate y value:
$y=\frac{-21}{17}$
Wait, correct subtraction: $15-36=-21$, $9y+8y=17y$, so $y=-1$ (correction: $15-36=-21$ → $17y=-21$ is error, actual: $36-15=21$, $-8y-9y=-17y=-21$ → $y=-1$)

Step4: Substitute y=-1 into 2x+3y=5

Solve for x:
$2x+3(-1)=5$
$2x-3=5$
$2x=8$
$x=4$

Answer:

B. (4, -1)