Question

1. \

$$\begin{cases} -3x - 4y = -1 \\\\ 3x - y = -4 \\end{cases}$$

Explanation:

Step1: Eliminate \(x\) by adding equations

Add the two equations \(-3x - 4y = -1\) and \(3x - y = -4\) together.
\((-3x - 4y)+(3x - y)=-1+(-4)\)
Simplify: \(-3x + 3x - 4y - y=-5\), so \(-5y = -5\).

Step2: Solve for \(y\)

Divide both sides of \(-5y = -5\) by \(-5\):
\(y=\frac{-5}{-5}=1\)

Step3: Substitute \(y = 1\) into one equation

Substitute \(y = 1\) into \(3x - y = -4\):
\(3x - 1=-4\)

Step4: Solve for \(x\)

Add 1 to both sides: \(3x=-4 + 1=-3\)
Divide by 3: \(x=\frac{-3}{3}=-1\)

Answer:

The solution to the system is \(x = -1\), \(y = 1\) (or as an ordered pair \((-1, 1)\))