Question

use the elimination method to solve the system\

$$\begin{cases}7a - 5b = 43\\\\12a + 8b = 24\\end{cases}$$

\\(a, b) = (\boxed{?})

Explanation:

Step1: Multiply equations to eliminate

Multiply the first equation \(7a - 5b = 43\) by 8: \(56a - 40b = 344\).
Multiply the second equation \(12a + 8b = 24\) by 5: \(60a + 40b = 120\).

Step2: Add the two new equations

Add \(56a - 40b = 344\) and \(60a + 40b = 120\):
\(56a + 60a - 40b + 40b = 344 + 120\)
\(116a = 464\)

Step3: Solve for \(a\)

Divide both sides by 116: \(a = \frac{464}{116} = 4\).

Step4: Substitute \(a = 4\) into \(12a + 8b = 24\)

\(12(4) + 8b = 24\)
\(48 + 8b = 24\)

Step5: Solve for \(b\)

Subtract 48: \(8b = 24 - 48 = -24\)
Divide by 8: \(b = \frac{-24}{8} = -3\).

Answer:

\((4, -3)\)