Question

question
find the solution of the system of equations.
\\(15x - 4y = -50\\)
\\(3x - 2y = -16\\)

Explanation:

Step1: Eliminate $x$ variable

Multiply the second equation by 5:
$$5\times(3x - 2y) = 5\times(-16) \implies 15x - 10y = -80$$

Step2: Subtract equations

Subtract the new equation from the first equation:
$$(15x - 4y) - (15x - 10y) = -50 - (-80)$$
$$15x - 4y -15x +10y = -50 +80$$
$$6y = 30$$

Step3: Solve for $y$

Divide both sides by 6:
$$y = \frac{30}{6} = 5$$

Step4: Substitute $y=5$ to find $x$

Plug $y=5$ into $3x - 2y = -16$:
$$3x - 2(5) = -16$$
$$3x -10 = -16$$
$$3x = -16 +10 = -6$$
$$x = \frac{-6}{3} = -2$$

Answer:

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