Question

4x - 3y = 2\
4x - 5y = -10

Explanation:

Step1: Label the equations

Let:
$4x - 3y = 2 \quad \text{(Equation 1)}$
$4x - 5y = -10 \quad \text{(Equation 2)}$

Step2: Eliminate $x$ via subtraction

Subtract Equation 2 from Equation 1 to cancel $4x$:
$(4x - 3y) - (4x - 5y) = 2 - (-10)$
Simplify the left and right sides:
$4x - 3y - 4x + 5y = 2 + 10$
$2y = 12$

Step3: Solve for $y$

Divide both sides by 2:
$y = \frac{12}{2} = 6$

Step4: Substitute $y=6$ into Equation 1

Plug $y=6$ into $4x - 3y = 2$:
$4x - 3(6) = 2$
$4x - 18 = 2$

Step5: Solve for $x$

Add 18 to both sides, then divide by 4:
$4x = 2 + 18 = 20$
$x = \frac{20}{4} = 5$

Answer:

$x=5$, $y=6$