Question

find the solution of the system of equations.
$2x - 9y = 38$
$4x + 5y = -16$

Explanation:

Step1: Eliminate x by multiplying first equation

Multiply the first equation \(2x - 9y = 38\) by 2 to get \(4x - 18y = 76\).

Step2: Subtract the two equations

Subtract the second equation \(4x + 5y = -16\) from the new first equation: \((4x - 18y) - (4x + 5y) = 76 - (-16)\). Simplify to \(-23y = 92\).

Step3: Solve for y

Divide both sides by -23: \(y = \frac{92}{-23} = -4\).

Step4: Substitute y into first equation

Substitute \(y = -4\) into \(2x - 9y = 38\): \(2x - 9(-4) = 38\), which simplifies to \(2x + 36 = 38\).

Step5: Solve for x

Subtract 36 from both sides: \(2x = 2\), then divide by 2: \(x = 1\).

Answer:

The solution is \(x = 1\), \(y = -4\)