Question

solve using elimination.
10x - 6y = 18
-x - y = 11
(□, □)

Explanation:

Step1: Multiply the second equation

To eliminate a variable, we can multiply the second equation \(-x - y = 11\) by 6 to make the coefficients of \(y\) opposite (or same) as in the first equation. So we get \(6\times(-x - y)=6\times11\), which simplifies to \(-6x - 6y = 66\).

Step2: Subtract the two equations

Now we have the first equation \(10x - 6y = 18\) and the new second equation \(-6x - 6y = 66\). Subtract the second equation from the first equation: \((10x - 6y)-(-6x - 6y)=18 - 66\). Simplifying the left side: \(10x - 6y + 6x + 6y = 16x\), and the right side: \(18-66=-48\). So we have \(16x=-48\).

Step3: Solve for x

Divide both sides of \(16x = - 48\) by 16: \(x=\frac{-48}{16}=-3\).

Step4: Substitute x into an equation

Substitute \(x = - 3\) into the second original equation \(-x - y = 11\). We get \(-(-3)-y = 11\), which simplifies to \(3 - y = 11\).

Step5: Solve for y

Subtract 3 from both sides: \(-y=11 - 3 = 8\), then multiply both sides by - 1: \(y=-8\).

Answer:

\((-3, -8)\)