Question

8 3x - 5y = -9
3x - 2y = -3

Explanation:

Step1: Label the equations

Let
$3x - 5y = -9 \quad \text{(Equation 1)}$
$3x - 2y = -3 \quad \text{(Equation 2)}$

Step2: Eliminate $x$ via subtraction

Subtract Equation 1 from Equation 2 to cancel $3x$:
$$(3x - 2y) - (3x - 5y) = -3 - (-9)$$
Simplify the left and right sides:
$$3x - 2y - 3x + 5y = -3 + 9$$
$$3y = 6$$

Step3: Solve for $y$

Divide both sides by 3:
$$y = \frac{6}{3} = 2$$

Step4: Substitute $y=2$ into Equation 2

Substitute $y=2$ to solve for $x$:
$$3x - 2(2) = -3$$
$$3x - 4 = -3$$

Step5: Solve for $x$

Add 4 to both sides, then divide by 3:
$$3x = -3 + 4 = 1$$
$$x = \frac{1}{3}$$

Answer:

$x=\frac{1}{3}$, $y=2$