+129930 3x + 2y + z = 7 (1)
5x + 5y + 4z = 3 (2)
3x + 2y + 3z = 1 (3)
The object, NSS, is to eliminate a variable and end up with 2 equations with two unknowns
We can choose any variable that we want......here....z seems easiest
Multiply the first equation by -4 and add it to equation 2
-12x - 8y - 4z = -28
5x + 5y + 4z = 3
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-7x - 3y = -25 → 7x + 3y = 25 (4)
Multiply the first equation by -3 and add it to to the 3rd equation
-9x - 6y - 3z = -21
3x + 2y + 3z = 1
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- 6x - 4y = -20 → 6x + 4y = 20 (5)
Multiply (4) by 4 and (5) by -3
28x +12 y = 100
-18x - 12y = -60 add these together
10x = 40 divide both sides by 10
x = 4
Using (5) to find y, we have
6(4) + 4y = 20
24 + 4y = 20 subtract24 from both sides
4y = -4 divide both sides by 4
y = - 1
And using 3x + 2y + 3z = 1 to find z, we have
3 (4) + 2 (-1) + 3z = 1
12 - 2 + 3z = 1
10 + 3z = 1 subtract 10 from both sides
3z = -9 divide both sides by
z = -3
So....{ x , y, z } = { 4, -1, -3 }
