Question

1. \

$$\begin{cases} 3x + 2y = -26 \\\\ 4x - 5y = -4 \\end{cases}$$

Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 5: \(5(3x + 2y) = 5(-26)\) → \(15x + 10y = -130\)
Multiply the second equation by 2: \(2(4x - 5y) = 2(-4)\) → \(8x - 10y = -8\)

Step2: Add the two new equations

\((15x + 10y) + (8x - 10y) = -130 + (-8)\)
Simplify: \(23x = -138\)

Step3: Solve for x

\(x = \frac{-138}{23} = -6\)

Step4: Substitute x = -6 into first equation

\(3(-6) + 2y = -26\) → \(-18 + 2y = -26\)

Step5: Solve for y

\(2y = -26 + 18 = -8\) → \(y = \frac{-8}{2} = -4\)

Answer:

The solution to the system is \(x = -6\), \(y = -4\)