Solve the following system of equations x1 2x2 x3 5 x1 x

Solve the following system of equations: x_1 - 2x_2 + x_3 = 5 -x_1 + x_2 - 4x_3 = -7 3x_1 + 3x_2 + x_3 = 4

Solution

Adding first two equations gives:

-2x2-3x3=-2

Subtracting three times first equation from last gives:

8x2-2x3=-11

Solving these two equations gives:

-14x3=-19

x3=19/14,x2=29/28

x1-2x2+x3=5

x1-29/14+19/14=5

x1-10/14=5

x1=5+5/7=40/7