Solve the system by substitution if possible
{ 8x+3y=40 16x+6y=41
a. (10, –5)
b. (–2, –8)
c. (–6,11)
d. (9, 2)
e. no solution; inconsistent system
Solve the system, if possible.
{9x + 3y + 4z = -94 5x−5y+2z=2 6x − 7y − 10z = 6
a. x=–7,y=–6,z=4
b. x=–6,y=–8,z=–4
c. x=6,y=8,z=4
d. x=–14,y=3,z=4
e. no solution; inconsistent system
+130560 8x+3y=40 16x+6y=41 if we multiply the first equation by 2 we get
16x + 6y = 80 but the second equation says that 16x + 6y = 41
Then 16x + 6y has two different values and this is impossible.......so......the answer is "e"
+130560 9x + 3y + 4z = -94 5x−5y+2z=2 6x − 7y − 10z = 6
Multiply the second equation by -2 and add it to the first
9x + 3y + 4z = -94
-10x+10y-4z = -4
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-x + 13y = - 98 (4)
Multiply the second equation by 5 and add it to the third
6x - 7y - 10z = 6
25x -25y + 10z = 10
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31x - 32y = 16 (5)
Multiply (4) by 31 and add to (5)
31x - 32y = 16
-31x + 403y = -3038
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371y = -3022 → y = -3022/371
And we can use (4) to find x
-x + 13 (-3022/371) = -98
x = 98 + 13(-3022/371) = -2928/371
And using the second equation to find z, we have
5(-2928/371) −5(-3022/371) +2z=2
2z = 2 - 5(-2928/371) + 5(-3022/371)
z = [2 - 5(-2928/371) + 5(-3022/371)] / 2 = 136/371
So.....the solutions are {x, y, z} = { -2928/371 , -3022/371 , 136/371 }
