find the solution of the system of equations.\n$9x + 2y = -38$\n$9x + 10y = 26$

Explanation:

Step1: Subtract the first equation from the second

$$ \begin{align*} (9x + 10y)-(9x + 2y)&=26-(-38)\ 9x + 10y - 9x - 2y&=26 + 38\ 8y&=64 \end{align*} $$

Step2: Solve for (y)

Divide both sides of (8y = 64) by (8): (y=\frac{64}{8}=8)

Step3: Substitute (y = 8) into the first equation

Substitute (y = 8) into (9x+2y=-38), we get (9x+2\times8=-38), which is (9x + 16=-38)

Step4: Solve for (x)

Subtract (16) from both sides: (9x=-38 - 16=-54) Divide both sides by (9): (x=\frac{-54}{9}=-6)

Answer:

(x=-6,y = 8)