Question

1. (a.ei.2, 5 points) given the following system of equations what is the solution for x? \

$$\begin{cases} 4x - 3y = 11 \\\\ 3x + 2y = -13 \\end{cases}$$

x = \underline{\quad\quad}

Explanation:

Step1: Eliminate y by scaling equations

Multiply the first equation \(4x - 3y = 11\) by 2: \(8x - 6y = 22\).
Multiply the second equation \(3x + 2y = -13\) by 3: \(9x + 6y = -39\).

Step2: Add the scaled equations

Add \(8x - 6y = 22\) and \(9x + 6y = -39\):
\((8x + 9x) + (-6y + 6y) = 22 + (-39)\)
\(17x = -17\).

Step3: Solve for x

Divide both sides by 17: \(x = \frac{-17}{17} = -1\).

Answer:

\(x = -1\)