Question

1. \

$$\begin{cases} 2x - 3y = 14 \\\\ x + 3y = -11 \\end{cases}$$

Explanation:

Step1: Add the two equations

We have the system of equations:

$$\begin{cases} 2x - 3y = 14 \\ x + 3y = -11 \end{cases}$$

Adding the two equations together to eliminate \(y\):
\((2x - 3y)+(x + 3y)=14+(-11)\)
Simplifying the left - hand side: \(2x - 3y+x + 3y=3x\)
Simplifying the right - hand side: \(14-11 = 3\)
So we get the equation \(3x=3\)

Step2: Solve for x

Divide both sides of the equation \(3x = 3\) by 3:
\(x=\frac{3}{3}=1\)

Step3: Substitute x into one of the original equations

Substitute \(x = 1\) into the second equation \(x + 3y=-11\):
\(1+3y=-11\)
Subtract 1 from both sides: \(3y=-11 - 1=-12\)
Divide both sides by 3: \(y=\frac{-12}{3}=-4\)

Answer:

The solution to the system of equations is \(x = 1,y=-4\)