Solve the system of linear equations. (If the system is dependent, express your answer in terms of t, where x = x(t), y = y(t), z = z(t), and w = t.

Question

Solve the system of linear equations. (If the system is dependent, express your answer in terms of t, where x = x(t),

 y = y(t),

 z = z(t),

 and w = t.

 If the system is inconsistent, enter INCONSISTENT.)

	x	+	y	−	z	−	w	=	14
2x	+	z	−	3w	=	31
x	−	y	+	4w	=	−25
3x	+	5y	−	z	−	w	=	32
(x, y, z, w) =

 

 

Answer 1

x + y - z - w = 14

2x + z - 3w = 31

x - y + 4w = -25

3x + 5y -z - w = 32

Eliminates z:

eq1 + eq2

eq2 + eq4

3x + y - 4w = 45

x - y + 4w = -25

5x + 5y - 4w = 63

Eliminates w:

eq1 + eq2

eq2 + eq2

4x = 20 -->x = 5

6x + 4y = 38

then 6(5) + 4y = 38

30 + 4y = 38

4y = 8

y = 2

Substitutes into eq 3:

5 - 2 + 4w = -25

3 + 4w = -25

4w = -28

w = -7

original First eq:

x + y - z - w = 14

5 + 2 - z - -7 = 14

14 - z = 14

z = 0

(x=5, y=2, z =0, w= -7}

yes it checks