Question

solve.
-9x - 6y = 6
-3x + 2y = 10
(□, □)
submit

Explanation:

Step1: Multiply the second equation

To eliminate a variable, multiply the second equation \(-3x + 2y = 10\) by 3. We get \(3\times(-3x + 2y)=3\times10\), which simplifies to \(-9x + 6y = 30\).

Step2: Add the two equations

Now we have the first equation \(-9x - 6y = 6\) and the new second equation \(-9x + 6y = 30\). Add them together: \((-9x - 6y)+(-9x + 6y)=6 + 30\). The \(y\)-terms cancel out: \(-18x=36\).

Step3: Solve for \(x\)

Divide both sides of \(-18x = 36\) by \(-18\): \(x=\frac{36}{-18}=-2\).

Step4: Substitute \(x\) into an equation

Substitute \(x = -2\) into the second original equation \(-3x + 2y = 10\). We get \(-3\times(-2)+2y = 10\), which simplifies to \(6 + 2y = 10\).

Step5: Solve for \(y\)

Subtract 6 from both sides: \(2y=10 - 6 = 4\). Then divide by 2: \(y=\frac{4}{2}=2\).

Answer:

\((-2, 2)\)