Question

which ordered pair is a solution to the system of linear equations?
$2x + 3y = 6$
$-3x + 5y = 10$
$\bigcirc\\ (0,2)$
$\bigcirc\\ (2,0)$
$\bigcirc\\ (3,2)$
$\bigcirc\\ (2,3)$

Explanation:

Step1: Eliminate x variable

Multiply first equation by 3: $6x + 9y = 18$
Multiply second equation by 2: $-6x + 10y = 20$
Add the two new equations:
$$(6x + 9y) + (-6x + 10y) = 18 + 20$$
$$19y = 38$$

Step2: Solve for y

$$y = \frac{38}{19} = 2$$

Step3: Substitute y=2 into first equation

$$2x + 3(2) = 6$$
$$2x + 6 = 6$$

Step4: Solve for x

$$2x = 6 - 6 = 0$$
$$x = 0$$

Answer:

(0,2)