<PRE><B>Question 190977</B>
A - B + C = 1
2A -2B = 0
3A + B -3C = 2
:
multiply the 1st equation by 2, subtract the 2nd equation
2A - 2B + 2C = 2
2A - 2B + 0C = 0
------------------ subtraction eliminates A &amp; B, find C
2C = 2
C = 1
:
Substitute 1 for C in the 1st and 3rd equations
A - B + 1 = 1
3A +B -3(1) = 2
:
A - B = 1 - 1
3A +B = 2 + 3
:
A - B = 0
3A +B = 5
------------Adding eliminates B
4A = 5
A = {{{5/4}}}
:
Find B using 2A - 2B = 0; therefore: B = A
B = {{{5/4}}}
:
Solution: A = {{{5/4}}}, B = {{{5/4}}}, C = 1
;
:
Check solution in the 3rd equation:
3A + B -3C = 2
3({{{5/4}}}) + {{{5/4}}} - 3(1) = 2
{{{15/4}}} + {{{5/4}}} - 3 = 2
{{{20/4}}} - 3 = 2
5 - 3 = 2</PRE>