Question

solve using elimination.
6x - 8y = 20
3x - 8y = 2
(\square, \square)

Explanation:

Step1: Subtract the second equation from the first

We have the system of equations:

$$
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$$

Subtract the second equation from the first: \((6x - 8y)-(3x - 8y)=20 - 2\)
Simplify the left - hand side: \(6x-8y - 3x + 8y=3x\)
Simplify the right - hand side: \(18\)
So we get \(3x=18\)

Step2: Solve for x

Divide both sides of the equation \(3x = 18\) by 3: \(x=\frac{18}{3}=6\)

Step3: Substitute x = 6 into one of the original equations

Let's substitute \(x = 6\) into the second equation \(3x-8y = 2\)
We have \(3\times6-8y=2\)
Simplify the left - hand side: \(18-8y = 2\)

Step4: Solve for y

Subtract 18 from both sides: \(-8y=2 - 18=-16\)
Divide both sides by - 8: \(y=\frac{-16}{-8}=2\)

Answer:

\((6,2)\)