Question

#1 find the value of x + y
-7x - 5y = -8
8x - 3y = -17

Explanation:

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

Multiply the first equation by 3: \(3(-7x - 5y) = 3(-8)\) → \(-21x - 15y = -24\)
Multiply the second equation by 5: \(5(8x - 3y) = 5(-17)\) → \(40x - 15y = -85\)

Step2: Subtract the two new equations

\((40x - 15y) - (-21x - 15y) = -85 - (-24)\)
\(40x - 15y + 21x + 15y = -85 + 24\)
\(61x = -61\)
\(x = -1\)

Step3: Substitute x into first equation

\(-7(-1) - 5y = -8\)
\(7 - 5y = -8\)
\(-5y = -15\)
\(y = 3\)

Step4: Calculate \(x + y\)

\(x + y = -1 + 3 = 2\)

Answer:

2