double the 1st: 14x - 6y + 8z = 36
using the 2nd: 13x + 6y + 8z = 30
add them
27x + 16y = 66 , #4
triple the 1st: 21x - 9y + 12z = 54
using the 3rd: 11x - 9y - 12z = 16
subtract them: 10x + 24z = 38
5x + 12z = 19 , #5
#4 times 3 ---> 81x + 48y = 198
#5 times 4 ---> 20x + 48y = 76
subtract:
61x = 122
x = 2
back into #5:
10+12z = 19
z = 9/12 = 3/4
back into #1
14 - 3y + 3 = 18
y = -1/3
notice, my method is not unique. There are several ways this could have been done using elimination.
I usually look over my numbers and decide which coefficients are the simplest to eliminate
I chose the y's because of the simple 3, 6 , 9 combination.
My second choice would have been the z's, since 4,8,12 are also nice multiples
My last choice would have been the x's.
7, 13, 11 are all prime, which usually is not so good in these types of problems
7x-3y+4z=18
13x+6y+8z=30
11x-9y-12z=16
Find x,y,z please show the solution pleaseee
1 answer
1 answer