solve using elimination.\n4x - 5y = -17\n2x + 9y = 3

Explanation:

Step1: Eliminate (x)

Multiply the second equation (2x + 9y=3) by (2) to get (4x+18y = 6). Now we have the system: (\begin{cases}4x-5y=-17\4x + 18y=6\end{cases}) Subtract the first equation from the second: ((4x+18y)-(4x - 5y)=6-(-17)) (4x+18y - 4x+5y=6 + 17) (23y=23)

Step2: Solve for (y)

Divide both sides of (23y = 23) by (23): (y=\frac{23}{23}=1)

Step3: Substitute (y = 1) into one of the original equations

Substitute (y = 1) into (2x+9y = 3) (2x+9\times1=3) (2x+9=3) Subtract (9) from both sides: (2x=3 - 9=-6) Divide both sides by (2): (x=\frac{-6}{2}=-3)

Answer:

(x=-3,y = 1)