solve by elimination

Question

x + 2y + 3z = 4

-3x + 2y +z = 12

-2x - 2y -4z = 14

Answer 1

Eliminates x:

row2 = 3*row1+row2

row3 = 2*row1 + row3

-------------------------

8y + 10z = 24

2y + 2z = 22

divides everything by 2:

4y + 5z = 12

y + z = 11

finally, -4 * bottom + top:

z = -32

y + -32 = 11

y = 43

x + 2y + 3z = 4

x + 2(43) + 3(-32) = 4

x + 86 - 96 = 4

x - 10 = 4

x = 14

x=14 y = 43 z = -32

check:

x + 2y + 3z = 14 + 2(43) + 3(-32)

= 14 + 86 - 96

= 14-10

= 4

-3x + 2y + z = -3(14) + 2(43) + -32

= -42 + 86 + -32

= 44 + -32

= 12

-2x-2y-4z = -2(14) - 2(43) - 4(-32)

= -28 - 86 + 128

= 100 - 86

= 14

Yes it checks

x=14 y = 43 z = -32

are the official answers