Question

2x - 5y = 2, 3x + 2y = 3; y = 8; (1, 0); (-6, -1); x = 2

Explanation:

Step1: Label the two equations

Let:
$$2x - 5y = 2 \tag{1}$$
$$3x + 2y = 3 \tag{2}$$

Step2: Eliminate $x$ via scaling

Multiply equation (1) by 3, equation (2) by 2:
$$6x - 15y = 6 \tag{3}$$
$$6x + 4y = 6 \tag{4}$$

Step3: Subtract equations to solve for $y$

Subtract (3) from (4):
$$(6x + 4y) - (6x - 15y) = 6 - 6$$
$$19y = 0 \implies y = 0$$

Step4: Substitute $y=0$ into equation (1)

$$2x - 5(0) = 2$$
$$2x = 2 \implies x = 1$$

Answer:

$(1, 0)$