Expert: Sherman D. - 11/13/2008

Question
QUESTION: I'm pretty much stumped. I've tried all methods I can think of and still can't get the answer. I would be grateful if someone can help me with this one.

5a-b+3c=5
2a+7b-2c=5
4a-5b-7c= -65

Thank you.

ANSWER: I'll be using Cramer's Rule

5a - b + 3c = 5
2a + 7b - 2c = 5
4a - 5b - 7c = -65

+++5,-1,+3:5
+++2,+7,-2:5
+4,-5,-7:-65

det = ((5 * 7 * -7) + (2 * -5 * 3) + (-1 * -2 * 4)) - ((4 * 7 * 3) + (2 * -1 * -7) + (-2 * -5 * 5))
det = (-245 - 30 + 8) - (84 + 14 + 50)
det = -267 - 148
det = -415

--------------------

++5,-1,+3
++5,+7,-2
-65,-5,-7

detA = ((5 * 7 * -7) + (5 * -5 * 3) + (-1 * -2 * -65)) - ((-65 * 7 * 3) + (5 * -1 * -7) + (-2 * -5 * 5))
detA = (-245 - 75 - 130) - (-1365 + 35 + 50)
detA = -450 + 1280
detA = 830

a = detA/det
a = 1250/-415
a = 830/-415
a = -2

----------------------------

++5,+5,+3
++2,+5,-2
+4,-65,-7

detB = ((5 * 5 * -7) + (5 * -2 * 4) + (3 * 2 * -65)) - ((4 * 5 * 3) + (5 * 2 * -7) + (-65 * -2 * 5))
detB = (-175 - 40 - 390) - (60 - 70 + 650)
detB = -605 - 640
detB = -1245

b = -1245/-415
b = 3

----------------------------

+++5,-1,+5
+++2,+7,+5
++4,-5,-65

detC = ((5 * 7 * -65) + (2 * -5 * 5) + (-1 * 5 * 4)) - ((4 * 7 * 5) + (2 * -1 * -65) + (5 * -5 * 5))
detC = (-2275 - 50 - 20) - (140 + 130 - 125)
detC = -2345 - 145
detC = -2490

c = -2490/-415
c = 6

ANS :

a = -2
b = 3
c = 6

whenever you would like to check your answers, just go to www.quickmath.com, click on Solve under Equations, then click Advanced, and type in your problem, making sure you have the right variables on the far right side, then click solve.

if you like, i can do this the long way by solving it a different way.

the reason i said that is because i don't know if you are familiar with Cramer's Rule.

If you aren't, this site will show you how to work your problem using Cramer's Rule.

http://www.college-cram.com/study/precalculus/presentations/439

---------- FOLLOW-UP ----------

QUESTION: I don't know much about the Cramer's Rule. All I know is, we have to do it the regular way.

Answer
5a - b + 3c = 5
2a + 7b - 2c = 5
4a - 5b - 7c = -65

5a - b + 3c = 5
-b = -5a - 3c + 5
b = 5a + 3c - 5

2a + 7(5a + 3c - 5) - 2c = 5
2a + 35a + 21c - 35 - 2c = 5
37a + 19c = 40

4a - 5(5a + 3c - 5) - 7c = -65
4a - 25a - 15c + 25 - 7c = -65
-21a - 22c = -90

so now we have

37a + 19c = 40
-21a - 22c = -90

Multiply top by 21 and bottom by 37

777a + 399c = 840
-777a - 814c = -3330

-415c = -2490
c = 6

37a + 19(6) = 40
37a = -74
a = -2

now that we have both "a" and "c"

b = 5a + 3c - 5
b = 5(-2) + 3(6) - 5
b = -10 + 18 - 5
b = 8 - 5
b = 3

ANS :
a = -2
b = 3
c = 6

However, if you go to www.quickmath.com and the answers don't turn out to be just like your answers, either you typed in something wrong, you did your math wrong, or you did your math right and you will have to work out the problems a different way until the correct work leads to the correct answer. I've done at least one of these many times. Mostly is that i either did the work wrong or i did them right but i had to work them a different way so that they turn out the way the should.