Blog: `-2x + 6y = -22, x + 2y = -9` Use matricies to solve the system of equations (if possible). Use Gauss-Jordan elimination.

Monday, April 18, 2011

Given ,

$\displaystyle-{2}{x}+{6}{y}=-{22},{x}+{2}{y}=-{9}$

A = $\displaystyle{\left[\matrix{-{2}&{6}\\{1}&{2}}\right]}$

and B = $\displaystyle{\left[\matrix{-{22}\\-{9}}\right]}$

so the augmented matrix is

[A B]= $\displaystyle{\left[\matrix{-{2}&{6}&-{22}\\{1}&{2}&-{9}}\right]}$

step 1. Divide row 1 by -2

$\displaystyle{\left[\matrix{{1}&-{3}&{11}\\{1}&{2}&-{9}}\right]}$

Step 2: Subtract row 1 from row 2

$\displaystyle{\left[\matrix{{1}&-{3}&{11}\\{0}&{5}&-{20}}\right]}$

Step 3: Divide row 2 by 5

$\displaystyle{\left[\matrix{{1}&-{3}&{11}\\{0}&{1}&-{4}}\right]}$

Step 4: Subtract (-3 × row 2) from row 1

$\displaystyle{\left[\matrix{{1}&{0}&-{1}\\{0}&{1}&{4}}\right]}$

so the

values of x , y are x= -1 y = -4

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