SOLUTION: I was going along just fine doing Systems of Linear Equations and inequalities by the addition method. All of a sudden I had fractions and I am so confused, I have come up with the

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I was going along just fine doing Systems of Linear Equations and inequalities by the addition method. All of a sudden I had fractions and I am so confused, I have come up with the      Log On


   

Question 12587: I was going along just fine doing Systems of Linear Equations and inequalities by the addition method. All of a sudden I had fractions and I am so confused, I have come up with the answers for a few of them, I don't know how, I just kept trying different things to multiply them by, but there has got to be something I am doing wrong. It is taking me 4 hours to do 20 problems and a whole sheet of paper just to answer 3 problems. Here is one I got to and completely went, HUH!!
2x/5 - y/2=13/2
3x/4 - y/5=17/2
Now, If i remember right, my instructor said that you wanted to find a number to multiply these all by, and to find a number that all 3 denominators would go into. So I used 10 for the 1st one. This is how I did it.
(10)2x/5 - (10)y/2=(10)13/2, and my answer for that one is
4x+5y=65, I don't know if this is right, or if it is, what to do next. Please Help!!!!!!!!!! Thank you!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are on the right track! Multiply the 1st equation by 10.
10%282x%2F5+-+y%2F2%29+=+10%2813%2F2%29
4x+-+5y+=+65
Multiply the 2nd equation by 20.
20%283x%2F4+-+y%2F5%29+=+20%2817%2F2%29
15x+-+4y+=+170
So, now you have:
4x+-+5y+=+65 and
15x+-+4y+=+170 Now you can solve these by any one of the accepted methods so let's try elimination.
Let's multiply the 1st equation by 4 (so we can get 20y) and the 2nd equation by 5 (so we can get 20y there too}. Then we'll subtract one equation from the other to eliminate the y terms.
16x+-+20y+=+260
75x+-+20y+=+850 Subtract the top one from the bottom one.
---------------------
59x+=+590 Divide both sides by 59.
x+=+10
From:4x+-+5y+=+65 rewrite as: 5y+=+4x+-+65 and substitute x = 10 and solve for y.
5y+=+4%2810%29+-+65
5y+=+40+-+65
5y+=+-25 Divide both sides by 5.
y+=+-5
The solution is: (10, -5)
Let's see what the graph looks like:
graph%28300%2C200%2C-4%2C15%2C-10%2C8%2C%284%2F5%29x-13%2C%2815%2F4%29x-%2885%2F2%29%29