Question

select the correct answer.
solve the system of equations below.
$5x + 2y = 9$
$2x - 3y = 15$
a. $(-3,12)$
b. $(-3,3)$
c. $(12,-3)$
d. $(3,-3)$

Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 3: \(3(5x + 2y)=3\times9\) → \(15x + 6y = 27\)
Multiply the second equation by 2: \(2(2x - 3y)=2\times15\) → \(4x - 6y = 30\)

Step2: Add the two new equations

\((15x + 6y)+(4x - 6y)=27 + 30\)
Simplify: \(19x = 57\)

Step3: Solve for x

Divide both sides by 19: \(x=\frac{57}{19}=3\)

Step4: Substitute x=3 into first equation

\(5(3)+2y = 9\) → \(15 + 2y = 9\)

Step5: Solve for y

Subtract 15: \(2y = 9 - 15=-6\)
Divide by 2: \(y=\frac{-6}{2}=-3\)

Answer:

D. \((3,-3)\)