Question

solve using elimination.
-8x + 6y = 12
7x - 2y = 9
(□, □)

Explanation:

Step1: Eliminate y by scaling equations

To eliminate \( y \), we can multiply the second equation \( 7x - 2y = 9 \) by 3. This gives us:
\( 3\times(7x - 2y)=3\times9 \)
\( 21x - 6y = 27 \)

Step2: Add the two equations

Now we add the first equation \( -8x + 6y = 12 \) and the new second equation \( 21x - 6y = 27 \) together:
\( (-8x + 6y)+(21x - 6y)=12 + 27 \)
Simplifying the left - hand side: \( -8x+21x+6y - 6y=13x \)
Simplifying the right - hand side: \( 39 \)
So we have \( 13x = 39 \)

Step3: Solve for x

Divide both sides of the equation \( 13x = 39 \) by 13:
\( x=\frac{39}{13}=3 \)

Step4: Substitute x into one of the original equations to solve for y

We substitute \( x = 3 \) into the second original equation \( 7x - 2y = 9 \):
\( 7\times3-2y = 9 \)
\( 21-2y = 9 \)
Subtract 21 from both sides: \( - 2y=9 - 21=-12 \)
Divide both sides by - 2: \( y=\frac{-12}{-2}=6 \)

Answer:

\((3, 6)\)