Question

find the solution of the system of equations.
$9x + 2y = 49$
$-3x + 5y = -5$

Explanation:

Step1: Eliminate x by scaling the second equation

Multiply the second equation \(-3x + 5y = -5\) by 3 to get \(-9x + 15y = -15\).

Step2: Add the two equations

Add \(9x + 2y = 49\) and \(-9x + 15y = -15\):
\((9x - 9x) + (2y + 15y) = 49 - 15\)
Simplify: \(17y = 34\).

Step3: Solve for y

Divide both sides by 17: \(y = \frac{34}{17} = 2\).

Step4: Substitute y into the first equation

Substitute \(y = 2\) into \(9x + 2y = 49\):
\(9x + 2(2) = 49\)
\(9x + 4 = 49\).

Step5: Solve for x

Subtract 4: \(9x = 45\).
Divide by 9: \(x = \frac{45}{9} = 5\).

Answer:

The solution is \(x = 5\), \(y = 2\) (or as an ordered pair \((5, 2)\)).