Question

find the solution of the system of equations.\

$$\begin{cases}x - 3y = -19\\\\-x - 4y = -16\\end{cases}$$

Explanation:

Step1: Add the two equations

Add the equations \(x - 3y = -19\) and \(-x - 4y = -16\) to eliminate \(x\).

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Step2: Solve for \(y\)

Divide both sides of \(-7y = -35\) by \(-7\).

$$ y = \frac{-35}{-7} = 5 $$

Step3: Substitute \(y = 5\) into the first equation

Substitute \(y = 5\) into \(x - 3y = -19\).

$$ x - 3(5) = -19\\ x - 15 = -19 $$

Step4: Solve for \(x\)

Add 15 to both sides of \(x - 15 = -19\).

$$ x = -19 + 15 = -4 $$

Answer:

\(x = -4\), \(y = 5\)