Question

solve using elimination.
-3x - 9y = 6
x - y = 10
(□, □)
submit

Explanation:

Step1: Multiply the second equation

To eliminate \(x\), multiply the second equation \(x - y = 10\) by \(3\). We get \(3(x - y)=3\times10\), which simplifies to \(3x - 3y = 30\).

Step2: Add the two equations

Now we have the first equation \(-3x - 9y = 6\) and the new second equation \(3x - 3y = 30\). Add them together: \((-3x - 9y)+(3x - 3y)=6 + 30\). The \(x\)-terms cancel out: \(-12y=36\).

Step3: Solve for \(y\)

Divide both sides of \(-12y = 36\) by \(-12\): \(y=\frac{36}{-12}=-3\).

Step4: Substitute \(y\) to find \(x\)

Substitute \(y = - 3\) into the second original equation \(x - y = 10\). So \(x-(-3)=10\), which simplifies to \(x + 3 = 10\). Subtract \(3\) from both sides: \(x=10 - 3 = 7\).

Answer:

\((7, -3)\)