Question

question
find the solution of the system of equations.
$4x - 6y = 32$
$2x + 3y = 4$

Explanation:

Step1: Eliminate y by adding equations

Multiply the second equation by 2, then add to the first equation.
First, multiply $2x + 3y = 4$ by 2: $4x + 6y = 8$
Add to $4x - 6y = 32$:
$$(4x - 6y) + (4x + 6y) = 32 + 8$$
$$8x = 40$$

Step2: Solve for x

Divide both sides by 8.
$$x = \frac{40}{8} = 5$$

Step3: Substitute x=5 into second equation

Plug $x=5$ into $2x + 3y = 4$ to solve for y.
$$2(5) + 3y = 4$$
$$10 + 3y = 4$$

Step4: Isolate and solve for y

Subtract 10 from both sides, then divide by 3.
$$3y = 4 - 10 = -6$$
$$y = \frac{-6}{3} = -2$$

Answer:

$x=5$, $y=-2$