Question

solve using elimination.
9x - 10y = -8
-3x + 9y = -3
(□, □)

Explanation:

Step1: Multiply the second equation by 3

To eliminate \(x\), we multiply the second equation \(-3x + 9y=-3\) by 3. This gives us:
\(3\times(-3x + 9y)=3\times(-3)\)
\(-9x + 27y=-9\)

Step2: Add the first equation to the new second equation

Now we add the first equation \(9x - 10y=-8\) to \(-9x + 27y=-9\):
\((9x - 9x)+(-10y + 27y)=-8 + (-9)\)
Simplifying both sides, we get:
\(0x + 17y=-17\)
\(17y=-17\)

Step3: Solve for \(y\)

Divide both sides of \(17y=-17\) by 17:
\(y=\frac{-17}{17}=-1\)

Step4: Substitute \(y = - 1\) into the first equation

Substitute \(y=-1\) into \(9x - 10y=-8\):
\(9x-10\times(-1)=-8\)
\(9x + 10=-8\)

Step5: Solve for \(x\)

Subtract 10 from both sides:
\(9x=-8 - 10\)
\(9x=-18\)
Divide both sides by 9:
\(x=\frac{-18}{9}=-2\)

Answer:

\((-2, -1)\)