# Math Help - Can't solve system

1. ## Can't solve system

Find the general solution of the following system. Indicate which variables are basic and which
are free.

-2x1 + 3x2 + 3x3 + 2x4 = -9
3
x1 - 4x2 + x3 = 5

-
5x1 + 7x2 + 2x3 -3/2x4 = -14

The answer that i got is wrong( Can anyone could help me to solve this please?

2. If you subtract line2 from line1 you get line3.

$-2x_1+3x_2+3x_3+2x_4-(3x_1-4x_2+x_3)=5x_1+7x_2+2x_3-\frac{3}{2}x_4$

$-5x_1+7x_2+2x_3+2x_4=5x_1+7x_2+2x_3-\frac{3}{2}x_4$

$2x_4-5x_1=5x_1-\frac{3}{2}x_4$

$\frac{7}{2}x_4=10x_1$

$x_4=\frac{20}{7}x_1$

$-2x_1+3x_2+3x_3+\frac{40}{7}x_1=\frac{26}{7}x_1+3x_ 2+3x_3=-9$

$3x_1-4x_2+x_3=5$

$5x_1+7x_2+2x_3-\frac{30}{7}x_1=\frac{5}{7}x_1+7x_2+2x_3=-14$

This is now 3 simultaneous equations in 3 unknowns,
which can now be solved in the usual way.