Question

solve using elimination.
10x + 9y = 2
-5x - 3y = 11
(□, □)

Explanation:

Step1: Multiply the second equation by 2

To eliminate \(x\), we multiply the second equation \(-5x - 3y = 11\) by 2. This gives us:
\(2\times(-5x - 3y)=2\times11\)
\(-10x - 6y = 22\)

Step2: Add the first equation and the new second equation

Now we add the first equation \(10x + 9y = 2\) and the equation we just got \(-10x - 6y = 22\):
\((10x + 9y)+(-10x - 6y)=2 + 22\)
Simplifying the left side: \(10x-10x + 9y-6y=3y\)
Simplifying the right side: \(24\)
So we have \(3y=24\)

Step3: Solve for \(y\)

Divide both sides of \(3y = 24\) by 3:
\(y=\frac{24}{3}=8\)

Step4: Substitute \(y = 8\) into the first equation to solve for \(x\)

Substitute \(y = 8\) into \(10x + 9y = 2\):
\(10x+9\times8 = 2\)
\(10x+72 = 2\)
Subtract 72 from both sides:
\(10x=2 - 72=-70\)
Divide both sides by 10:
\(x=\frac{-70}{10}=-7\)

Answer:

\((-7, 8)\)