Question

2x + 3y = 1
4x + 5y = -5

Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by 2:
$$2(2x + 3y) = 2\times1 \implies 4x + 6y = 2$$

Step2: Subtract second equation

Subtract $4x + 5y = -5$ from the new equation:
$$(4x + 6y) - (4x + 5y) = 2 - (-5)$$
$$y = 7$$

Step3: Solve for $x$

Substitute $y=7$ into first equation:
$$2x + 3(7) = 1$$
$$2x + 21 = 1$$
$$2x = 1 - 21 = -20$$
$$x = \frac{-20}{2} = -10$$

Answer:

$x=-10$, $y=7$