We are working on solving systems using the method of elimination. There are three problems that I'm confused on because they involve fractions. If you could please show me how to solve each problem it would be greatly appreciated! Include all of your work too please. And I know this is a lot of work so there will be a best answer chosen! Thanks!
x/4 + y/6 = 1 x - y = 3
(x+3)/4 + (y-1)/3 = 1 2x - y = 5
(x-1)/2 + (y+2)/3 = 4 x - 2y = 5
2010-10-07T13:24:20Z
Never mind! Something just clicked in my brain and I solved them all! Thanks anyway!
Ari2010-10-07T13:30:55Z
Favorite Answer
1. u can use substitution
x/4 + y/6 = 1 x - y = 3
multiply top equation by 12 to clear the fractions
3x + 2y = 12 x - y = 3
multiply bottom by 2
3x + 2y = 12 2x -2y = 6
add
5x = 18
x = 18/5.
and therefore x = 3+y --> 18/5 = 3 + y --> y = 3/5
Your first system is below. To clear the fractions lets multiply the top equation by 12. This has nothing to do with solving for the solution but to get rid of the denominators. I do so we get
12(x/4 + y/6 = 1) x - y = 3
3x + 2y = 12 x - y = 3
Multiply second equation by 2 and add to the first equation and we get
3x + 2y = 12 2x - 2y = 6
5x = 18
x = 18/5 and to find plug this into either of the original equtions and solve for y. Let's chose the second equation and we get
18/5 - y = 3
- y = - 3/5
y = 3/5 so your solution is (18/5, 3/5)
Problem 2
Just like first problem multiply top equation by 12 to clear fractions and we get
12((x+3)/4 + (y-1)/3 = 1) 2x - y = 5
3(x + 3) + 4(y - 1) = 12 2x - y = 5
3x + 9 + 4y - 4 = 12 2x - y = 5
3x + 4y = 7 2x - y = 5
Multiply second equation by 4 and add to first eqation and we get
3x + 4y = 7 8x - 4y = 20
11x = 27 x = 27/11 now plug this back into either of the original equations and solve for y. Use second equation and we get
2(27/11) - y = 5
54/11 - y = 5
- y = 55/11 - 54/11
- y = 1/11
y = - 1/11 so the solution is (27/11, - 1/11)
The last system multiply the first equation by 6 to clear fractions
6((x-1)/2 + (y+2)/3 = 4) x - 2y = 5
3(x - 1) + 2(y + 2) = 24 x - 2y = 5
3x - 3 + 2y + 4 = 24 x - 2y = 5
3x + 2y = 23 x - 2y = 5
Just add the equations and we get
4x = 28
x = 7 and substituting back into one of the original equations. Lets chose the second and we get