Question

solve using elimination.
-2x - 5y = 11
6x + 2y = 6
(\boxed{ }, \boxed{ }))

Explanation:

Step1: Multiply first equation

To eliminate \(x\), multiply the first equation \(-2x - 5y = 11\) by \(3\).
\(3\times(-2x - 5y)=3\times11\)
\(-6x - 15y = 33\)

Step2: Add to second equation

Add the new first equation \(-6x - 15y = 33\) to the second equation \(6x + 2y = 6\).
\((-6x + 6x)+(-15y + 2y)=33 + 6\)
\(-13y = 39\)

Step3: Solve for \(y\)

Divide both sides by \(-13\):
\(y=\frac{39}{-13}=-3\)

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

Substitute \(y = -3\) into the second equation \(6x + 2y = 6\):
\(6x + 2\times(-3)=6\)
\(6x - 6 = 6\)
Add \(6\) to both sides: \(6x = 12\)
Divide by \(6\): \(x = 2\)

Answer:

\((2, -3)\)