Question

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

Explanation:

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

Multiply the first equation by 3 and the second by 2 to make coefficients of y opposites:
$$3(5x + 2y) = 3(9) \Rightarrow 15x + 6y = 27$$
$$2(2x - 3y) = 2(15) \Rightarrow 4x - 6y = 30$$

Step2: Add the two new equations

Add the equations to eliminate y:
$$(15x + 6y) + (4x - 6y) = 27 + 30$$
$$19x = 57$$

Step3: Solve for x

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

Step4: Substitute x = 3 into first equation

Substitute x = 3 into \(5x + 2y = 9\):
$$5(3) + 2y = 9$$
$$15 + 2y = 9$$

Step5: Solve for y

Subtract 15 from both sides:
$$2y = 9 - 15 = -6$$
Divide by 2:
$$y = \frac{-6}{2} = -3$$

Answer:

A. (3, -3)