SOLUTION: solve the system of equation by using any method 4a+3b+c=17, a-3b+2c=3, 11a-2b+3c=36

Algebra ->  Test -> SOLUTION: solve the system of equation by using any method 4a+3b+c=17, a-3b+2c=3, 11a-2b+3c=36      Log On


   

Question 935789: solve the system of equation by using any method 4a+3b+c=17, a-3b+2c=3, 11a-2b+3c=36
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4.00 a + 3.00 b + 1.00 c = 17.00 -------------- 1
1.00 a -3.00 b 2.00 c = 3.00 -------------- 2
11.00 a -2.00 b + 3.00 c = 36.00 -------------- 3

consider equation 1 &2 Eliminate b
Multiply 1 by 1.00 -5.00
Multiply 2 by 1.00 4.00
we get
4.00 a + 3.00 b + 1.00 c = 17
1.00 a -3.00 b + 2.00 c = 3
Add the two
5.00 a 0.00 b + 3.00 c = 20 ------------- 4
consider equation 2 & 3 Eliminate b
Multiply 2 by 2.00
Multiply 3 by -3.00
we get
2.00 a -6.00 b + 4.00 c = 6.00
-33.00 a + 6.00 b -9.00 c = -108.00
Add the two
-31.00 a + 0.00 b + -5.00 c = -102.00 -------------5 5
Consider (4) & (5) Eliminate a
Multiply 4 by -31.00
Multiply (5) by 5.00
we get
-155.00 a -93.00 c = -620.00
-155.00 a -25.00 c = -510.00
Add the two
0.00 a -118.00 c = -1,130.00
/ -118.00
c = 9.58
-31.00 x + -5.00 z= -102.00
-31.00 x + -47.88 = -102.00
x = 1.75
Plug x & z in eq (1)
4.00 x + 3.00 y + 1.00 z = 17.00 -------------- 1
6.98 + 3.00 y + 9.58 = 17.00
3.00 y = 0.44
y = 0.15
x= 1.75 y= 0.15 z= 9.58