Question

solve using elimination.
x - 6y = 20
-3x + 8y = -20
(\boxed{ }, \boxed{ }))

Explanation:

Step1: Eliminate \(x\) by multiplying first equation

Multiply the first equation \(x - 6y = 20\) by \(3\) to get \(3x - 18y = 60\).

Step2: Add the two equations

Add the new equation \(3x - 18y = 60\) and the second equation \(-3x + 8y = -20\):

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Step3: Solve for \(y\)

Divide both sides by \(-10\): \(y = \frac{40}{-10} = -4\).

Step4: Substitute \(y\) into first equation

Substitute \(y = -4\) into \(x - 6y = 20\):
\(x - 6(-4) = 20\)
\(x + 24 = 20\)

Step5: Solve for \(x\)

Subtract \(24\) from both sides: \(x = 20 - 24 = -4\).

Answer:

\((-4, -4)\)