# Math Help - solve linear system

1. ## solve linear system

solve and check

a+b+3c=12
2a+b+3c=14
a-b+4c=13

2. Originally Posted by nipun
solve and check

a+b+3c=12
2a+b+3c=14
a-b+4c=13

did u try to find the value of each variables which is a,b and c?

wat did i got is

a=2
b=1
c=3

3. how did you get the value of a,b, and c

can you plese tell me how did you find it?

4. Hi
solve and check

a+b+3c=12
2a+b+3c=14
a-b+4c=13

$\left\{ \begin{tabular}{lr}
a+b+3c=12 & (1)\\
2a+b+3c=14 & (2)\\
a-b+4c=13 &(3)
\end{tabular}\right.$

$(2)-(1)$ gives us the value of $a$ then $(2)+(3)$ gives us the value of $c$ and finally $(1)$ gives us the value of $b$.

5. Originally Posted by nipun
how did you get the value of a,b, and c

can you plese tell me how did you find it?
lets say

a+b+3c=12 (1)
2a+b+3c=14 (2)
a-b+4c=13 (3)

step 1

equation (1)-equation (3)

u will get
c=1+2b (4)

step 2
equation (1) multiply by 2

u will get: 2a+2b+6c=24 (5)

thus:

equation (5) -equation (2) and u will get;

b=10-3c

substitute b=10-3c into equation (4) and u will get the value of c

since one variables is known then it will easy to determine others