Answer:
X=7 Y=2
I will lead you through it and show you how you can find x through eliminating y, and finding y through eliminating x! So, both ways! :)
Explanation:
When looking to use the elimination method, either all x OR y coefficients must be equal before finding one or another. That might sound a little confusing so let me explain!
Finding x by eliminating y: (they already set it up for us, this way!)
6x+6y=54 6y and -6y will cancel each other out!
2x - 6y= 2
6x=54 Add both lines!
2x=2
8x=56 Now, divide 8 on both sides to find x!
x=7 The product is x equals 7! Plug into a line to find y!
6(7)+6y=54
42+6y=54 Subtract both sides by 42
6y=12 Divide both sides by 6
y=2
So, X=7 and Y=2 ! To check that this is true, plug both variables into one line!
2(7)-6(2)=2
14-12=2
2=2 2 equals 2, so this is true! Lets check the other line to make
sure!
6(7)+6(2)=54
42+12=54
54=54 Yes, this is also true! That means we found the true value of the variables. :)
Finding y by eliminating x: Now, how do we find X and Y using the elimination method if the terms are not equal? We will continue to use this problem since it meets the standards of unequal terms! However, we will find y by eliminating x!
We must get the x terms to be equal to they can cancel each other out! So, we will multiply a line by a certain variable until it matches the x term on the other line. We will multiply line 2 until it matches line 1's x term, but make sure the signs (positive/negative) are opposite so they cancel out! In other problems, one line's term may not be able to be multiplied until it reaches its term since it is not a factor of it! So, both lines would be multiplied b a specific number until they have a common multiple! Confusing? Just focus on the underlined portion of this paragraph as that is what you will need for this question. Lets work hard now! :)
6x+6y=54 Multiply line 2 by -3 so the x term will be cancel out line 1's x!
2x - 6y= 2
6x+6y=54
(2x - 6y= 2) -3 Yes, all of it!
6x+6y=54
-6x+18y=-6 Add both lines
24y=48 Divide 24 by both sides!
y=2 y is equivalent to 2! Plug value into a line!
6x+6(2)=54
6x+12=54 Subtract 12 on both sides!
6x=42 Divide 6 on both sides.
x=7 X is equal to 7!
So, X=7 and Y=2 , just like we found and even checked before! I hope this helped. Elimination method is my favorite method and overall favorite lesson in Algebra, for me, since it is pretty easy once you get a hang of it! Goodluck all! :)