Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + y − 2z = −3
x + 3y − z = −4
3x + 4y − z = 5
(x, y, z) =

x = -0.6

y = 2.2

z = 2

Step-by-step explanation:

2x + y - 2z = -3

x + 3y - z = 4

3x + 4y - z = 5

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)

21-2-3

13-14

34-15

R1 / 2 → R1 (divide the 1 row by 2)

10.5-1-1.5

13-14

34-15

R2 - 1 R1 → R2 (multiply 1 row by 1 and subtract it from 2 row); R3 - 3 R1 → R3 (multiply 1 row by 3 and subtract it from 3 row)

10.5-1-1.5

02.505.5

02.529.5

R2 / 2.5 → R2 (divide the 2 row by 2.5)

10.5-1-1.5

0102.2

02.529.5

R1 - 0.5 R2 → R1 (multiply 2 row by 0.5 and subtract it from 1 row); R3 - 2.5 R2 → R3 (multiply 2 row by 2.5 and subtract it from 3 row)

10-1-2.6

0102.2

0024

R3 / 2 → R3 (divide the 3 row by 2)

10-1-2.6

0102.2

0012

R1 + 1 R3 → R1 (multiply 3 row by 1 and add it to 1 row)

100-0.6

0102.2

0012

x = -0.6

y = 2.2

z = 2

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.