# MATH HW PLZ HELP!!!!?

The first one tells me to solve the equation using elimination and/or substitution.

2x - 3y + z = 10

3x - 8y +2z =11

-x + 5y- 3z = 15

The second question is asking to solve the system using Cramer's Rule.

3x - 7y + 4z = 11

x + y - z = 4

2x - 6y + z = 15

Thank you for all your help =]!

Relevance

Lets eliminate x first. Take the first 2 equations.

3 * (2x - 3y + z = 10)

-2 * (3x - 8y +2z =11)

=> 9y - 16y + 3z - 4z = 30 - 22

-7y -z = 8

Now do it with the last 2 equations.

1 * (3x - 8y +2z =11)

+3 *(-x + 5y- 3z = 15)

=> -8y + 15y + 2z -9z = 11 + 45

7y -7z = 56

You can add the 2 results to cancel y

-8z = 64

z = -8

Subbing in to -7y -z = 8

-7y - (-8) = 8

-7y = 0

y = 0

Subbing into 2x - 3y + z = 10

2x - 3*0 + -8 = 10

2x = 18

x = 9

(x,y,z) = (9, 0 -8)

A quick check shows that this satisfies all the equations (plug them back in all 3 equations to check).

==========

Note, determinant of

a b c

d e f

g h i

= aei + bfg + cdh - gec - hfa - idb

x = det(

11 7 4

4 1 -1

15 -6 1)/

det(

3 7 4

1 1 -1

2 -6 1)

= -344/-68

= 86/17

= 5 1/17 ~ 5.059

y = 52 / -68

= -13 / 17

z = -20/68

= -5/17