Question

find the solution of the system of equations.
10x - 2y = 44
-2x - 9y = 10

Explanation:

Step1: Simplify the first equation

Divide the first equation \(10x - 2y = 44\) by 2, we get \(5x - y = 22\), then express \(y\) in terms of \(x\): \(y = 5x - 22\).

Step2: Substitute \(y\) into the second equation

Substitute \(y = 5x - 22\) into the second equation \(-2x - 9y = 10\), we have \(-2x - 9(5x - 22) = 10\).
Expand the equation: \(-2x - 45x + 198 = 10\).
Combine like terms: \(-47x + 198 = 10\).
Subtract 198 from both sides: \(-47x = 10 - 198 = -188\).
Divide both sides by -47: \(x = \frac{-188}{-47} = 4\).

Step3: Find the value of \(y\)

Substitute \(x = 4\) into \(y = 5x - 22\), we get \(y = 5\times4 - 22 = 20 - 22 = -2\).

Answer:

The solution of the system of equations is \(x = 4\), \(y = -2\)