xa+3xb+xc=42xa+2xb+xc=−12xa+3xb+xc=3
The augmented matrix is
A=⎝⎛1223231114−13⎠⎞ R2=R2−2R1
⎝⎛1023−431−114−93⎠⎞ R3=R3−2R1
⎝⎛1003−4−31−1−14−9−5⎠⎞ R2=R2/(−4)
⎝⎛10031−311/4−149/4−5⎠⎞ R1=R1−3R2
⎝⎛10001−31/41/4−1−11/49/4−5⎠⎞ R3=R3+3R2
⎝⎛1000101/41/4−1/4−11/49/47/4⎠⎞ R3=−4R3
⎝⎛1000101/41/41−11/49/4−7⎠⎞ R1=R1−R3/4
⎝⎛10001001/41−19/4−7⎠⎞ R2=R2−R3/4
⎝⎛100010001−14−7⎠⎞
Then xa=−1,xb=4,xc=−7.
The solution is (−1,4,−7).
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