Use matrices to solve the system of equation. { 3x-2y+4z=4, x+y+z=3, 6x-2y-3z=10}

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Solve the system of equations. If the system has no solution, say it is inconsistent. (1) x + y + z = 3,(2) x - z = 1,(3) y - z = -4

Adding (1) and (2) leads to
(x+y+z)+(x-z)=3+1
2x+y=4
(4) y=4-2x

Adding (1) and (3) leads to
(x+y+z)+(y-z)=3-4
x+2y=-1

Replacing y with (4) leads to the solution for x:
x+2(4-2x)=-1
x+8-4x=-1
-3x=-9
x=3

Using x we can find y:
y=4-2x=4-2(3)=4-6=-2
y=-2 

Next we find z:
x+y+z=3
3-2+z=3
-2+z=0
z=2 

solution: (3, -2, 2)

Solve by back substitution. x = -2, x + y + z = -1, 2x + 2z = 0 Thank you

Solve by back substitution. x = -2 x + y + z = -1 2x + 2z = 0 Thank you

Your Answer:

1---> x = -2
2---> x + y + z = -1
3---> 2x + 2z = 0

3---> 2(-2)+2z=0
2z=4
z=2

2---> (-2)+y+(2)=-1
y=-1

solution: (-2,-1,2)

Solve the system of equations

The following matrix is is row-echelon form and represent a linear system. Solve the system using backward substitution. Write the solution as an ordered triple. [[ 1 1 -1 5][ 0 1 -1 2][ 0 0 1 1]]

z=1 
y-z=2
y-1=2
y=3 
x+y-z=5
x+3-1=5
x=3 
:)

Solve: x+y+z=6, 2x-y+z=3, 3x-z=0}

from 3: 
z=3x 
1 plus 2: 
(2x-y+z)+(x+y+z)=3+6 
3x+2z=9 
3x+2(3x)=9 
9x=9 
x=1 
so z=3 
from 1: 
x+y+z=1+y+3=6 
y+4=6 
y=2 

Solution: (1,2,3) 


:)

Timmy enjoys playing old-fashioned video games. He found 3 game systems on eBay and wants to purchase a Nintendo game system, an Atari game system, and a Sega arcade game system. The Sega system costs $600 more than the sum of the Atari and the Nintendo systems. All together, the three game systems cost $11,000. The Atari system costs $1100 less than the Nintendo. Determine how much Timmy paid for each game system.

1 S=N+A+600
2 N+S+A=11000
3 A=N-1100 

A=2050
N=3150
S=5800

Derive a quadratic equation using the following points: (1, -4), (2, -5), (3, -10)

y = ax^2+bx+c 
(1) (1, -4) -> -4=a+b+c , 
(2) (2, -5) -> -5= 4a+2b+c, 
(3) (3, -10) -> -10=9a+3b+c 

(2)-(1): 
-5+4=4a-a+2b-b+c-c 
-1=3a+b (or 3a+b=-1) 
(3)-(1): 
-6=8a+2b (or 4a+b=-3) 

taking the difference of these 2 we get 

4a-3a+b-b=-3+1 (or a=-2) 

and thus b=5 
Now from (1):
-4=-2+5+c (so c=-7) 



y=-2x^2+5x+-7 

:)