SOLUTION: How to do the System of equations. It says solve the system of equations a) 2x+3y+7z=13 b) x+3y+5z=20 3x+2y-5z=-22 y-4z=-16

Algebra ->  Expressions-with-variables -> SOLUTION: How to do the System of equations. It says solve the system of equations a) 2x+3y+7z=13 b) x+3y+5z=20 3x+2y-5z=-22 y-4z=-16       Log On


   



Question 729957: How to do the System of equations. It says solve the system of equations
a) 2x+3y+7z=13 b) x+3y+5z=20
3x+2y-5z=-22 y-4z=-16
5x+7y-3z=-28 3x+2y+9z=36

Answer by MathLover1(20850) About Me  (Show Source):
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a)
2x%2B3y%2B7z=13........eq. 1
3x%2B2y-5z=-22........eq. 2
5x%2B7y-3z=-28........eq. 3
________________________
2x%2B3y%2B7z=13........eq. 1 ..both multiply: eq1 by 3, eq 2 by 2
3x%2B2y-5z=-22........eq. 2
6x%2B9y%2B21z=39........eq. 1
6x%2B4y-10z=-44........eq. 2 .......subtract
______________________
6x%2B9y%2B21z-%286x%2B4y-10z%29=39-%28-44%29
6x%2B9y%2B21z-6x-4y%2B10z=39%2B44
5y%2B31z=83......eq. 1a

3x%2B2y-5z=-22........eq. 2 ...both multiply: eq2 by 5, eq 3 by 3
5x%2B7y-3z=-28........eq. 3
________________________
15x%2B10y-25z=-110........eq. 2
15x%2B21y-9z=-84........eq. 3
________________________.......subtract
15x%2B10y-25z-%2815x%2B21y-9z%29=-110-%28-84%29
15x%2B10y-25z-15x-21y%2B9z%29=-110%2B84
-11y-16z=-26......eq. 2a
take eq. 1a and 2a
5y%2B31z=83......eq. 1a....both multiply: eq1a by 11, eq 2a by 5
-11y-16z=-26......eq. 2a
_____________________________
55y%2B341z=913......eq. 1a.
-55y-80z=-130......eq. 2a
_____________________________...add
55y%2B341z%2B%28-55y-80z%29=913%2B%28-130%29
55y%2B341z-55y-80z=913-130
341z-80z=783
261z=783
z=783%2F261
highlight%28z=3%29
now go back to 55y%2B341z=913......eq. 1a., plug in z and solve for y
55y%2B341%2A3=913
55y%2B1023=913
55y=913-1023
55y=-110
y=-110%2F55
highlight%28y=-2%29

now go back to 2x%2B3y%2B7z=13........eq. 1., plug in y and z and solve for x
2x%2B3%28-2%29%2B7%2A3=13........eq. 1
2x-6%2B21=13
2x%2B15=13
2x=13-15
2x=-2
x=-2%2F2
highlight%28x=-1%29


b)
x%2B3y%2B5z=20........eq. 1
y-4z=-16.............eq. 2
3x%2B2y%2B9z=36........eq. 3
________________________
3x%2B9y%2B15z=60........eq. 1 ..multiply: eq1 by 3,
3x%2B2y%2B9z=36........eq. 3 ...subtract
______________________
3x%2B9y%2B15z-%283x%2B2y%2B9z%29=60-36
3x%2B9y%2B15z-3x-2y-9z=24
7y%2B6z=24.........................eq. 1a
take
7y%2B6z=24.........................eq. 1a
y-4z=-16.............eq. 2 ............multiply by 7 and subtract
______________________________
7y%2B6z=24.........................eq. 1a
7y-28z=-112.............eq. 2
____________________________subtract
7y%2B6z-%287y-28z%29=24-%28-112%29
7y%2B6z-7y%2B28z=24%2B112
34z=136
z=136%2F34
highlight%28z=4%29
go back to
y-4z=-16.............eq. 2 , plug in z and solve for y
y-4%2A4=-16
y-16=-16
y=-16%2B16
highlight%28y=0%29
go to x%2B3y%2B5z=20........eq. 1 plug in y and z and solve for x

x%2B3%2A0%2B5%2A4=20.
x%2B0%2B20=20
x=20-20
highlight%28x=0%29