Question

solve using elimination.
-4x - 3y = -4
-8x - 4y = 8
(\boxed{ }, \boxed{ })

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), we multiply the first equation \(-4x - 3y = -4\) by 2. This gives us:
\(2\times(-4x - 3y)=2\times(-4)\)
\(-8x - 6y = -8\)

Step2: Subtract the second equation

Now we have two equations:

1. \(-8x - 6y = -8\)
2. \(-8x - 4y = 8\)

Subtract the second equation from the first equation:
\((-8x - 6y)-(-8x - 4y)=-8 - 8\)
Simplify the left side: \(-8x - 6y + 8x + 4y=-2y\)
Simplify the right side: \(-16\)
So, \(-2y=-16\)

Step3: Solve for \(y\)

Divide both sides of \(-2y = -16\) by \(-2\):
\(y=\frac{-16}{-2}=8\)

Step4: Substitute \(y\) into first equation

Substitute \(y = 8\) into the first original equation \(-4x - 3y = -4\):
\(-4x - 3\times8=-4\)
\(-4x - 24=-4\)

Step5: Solve for \(x\)

Add 24 to both sides:
\(-4x=-4 + 24\)
\(-4x = 20\)
Divide both sides by \(-4\):
\(x=\frac{20}{-4}=-5\)

Answer:

\((-5, 8)\)