Question

1. $-8a - 5b = -27$

$7a + 6b = 22$

Explanation:

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

Multiply the first equation \(-8a - 5b = -27\) by 6: \(6(-8a - 5b) = 6(-27)\) → \(-48a - 30b = -162\)
Multiply the second equation \(7a + 6b = 22\) by 5: \(5(7a + 6b) = 5(22)\) → \(35a + 30b = 110\)

Step2: Add the two new equations

\((-48a - 30b) + (35a + 30b) = -162 + 110\)
Simplify: \(-13a = -52\)

Step3: Solve for a

Divide both sides by \(-13\): \(a = \frac{-52}{-13} = 4\)

Step4: Substitute a = 4 into one of the original equations (e.g., \(7a + 6b = 22\))

\(7(4) + 6b = 22\) → \(28 + 6b = 22\)

Step5: Solve for b

Subtract 28: \(6b = 22 - 28 = -6\)
Divide by 6: \(b = \frac{-6}{6} = -1\)

Answer:

\(a = 4\), \(b = -1\)