Question

1. solve the system of linear equations.

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

Explanation:

Step1: Solve for x from the second equation

From \( x + 5y = -4 \), we get \( x = -4 - 5y \).

Step2: Substitute x into the first equation

Substitute \( x = -4 - 5y \) into \( 3x - 2y = 5 \):
\( 3(-4 - 5y) - 2y = 5 \)

Step3: Simplify and solve for y

Expand: \( -12 - 15y - 2y = 5 \)
Combine like terms: \( -12 - 17y = 5 \)
Add 12 to both sides: \( -17y = 17 \)
Divide by -17: \( y = -1 \)

Step4: Substitute y back to find x

Substitute \( y = -1 \) into \( x = -4 - 5y \):
\( x = -4 - 5(-1) = -4 + 5 = 1 \)

Answer:

The solution to the system is \( (1, -1) \) (assuming the option \((1,1)\) might be a typo, and the correct solution is \( x = 1, y = -1 \)). If we were to check the options given (maybe for a related problem like finding a value from the solution), but based on solving the system, the solution is \( x = 1 \), \( y = -1 \).