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NotSoSmart  Oct 13, 2017
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 #1
avatar+76972 
+3

x +  5y  - 4z  = -10    multiply through by  -2   →   -2x - 10y + 8z  = 20   (1)  

2x - y + 5z  =  -9         (2)

2x  - 10y - 5z  =   0     (3)

 

Add  (1)  and (2)  ......this gives

-11y  + 13z  =  11      (4)

 

Add (1)  and (3).....this gives

-20y + 3z  = 20      (5)

 

Multiply  (4)  by   3   and (5)  by -13   and we have

-33y + 39z  = 33

260y - 39z = -260        add these

 

227 y  = -227          divide both sides by 227

y  = -1

 

Subbing this into  (4)  gives that     -11(-1) + 13z = 11   → 11 + 13z  =11 

Subtract 11 from both sides →   13z  = 0         which implies that z  =0

 

Subbing these values into  (2)   we have that

2x - (-1) + 5(0)  = -9

2x + 1  =  -9

2x  = -10     divide by 2

x  = -5

 

So  { x, y, z}  =  { -5, -1, 0 }

 

 

 

cool cool cool

 
CPhill  Oct 13, 2017
 #2
avatar+76972 
+3

2x  - y  + z  =  - 4

              z   =   5

-2x  + 3y  - z  = -10

 

Since we know that z  = 5......put this into equations one and three and we have

 

2x - y  + 5  = -4  →   2x  - y   = -9  →    y  = 2x  +  9    (4)

-2x + 3y  -5  = -10  → - 2x + 3y = -5    (5)

 

Sub  (4)  into (5)  for y   and we have that

-2x + 3 [2x + 9]  = -5

-2x + 6x + 27  = -5    subtract 27 from both sides

4x  = -32       divide both sides by 4

x  = -8

 

Put this into (4)  to find y

y = 2(-8) + 9

y = -16 + 9

y = -7

 

So  ...  { x, y, z }  = { -8, -7, 5 }

 

 

cool cool cool

 
CPhill  Oct 13, 2017
 #3
avatar+76972 
+3

 

Here's the last one....it's could be little tricky, NSS.....but.....turns out....it isn't  !!!

 

Let  x  be the lbs  of peanuts, y be the lbs of almonds and z be the lbs of raisins

Since we have 11 lbs total, one of the equations is

x  + y +   z  = 11

 

And we need twice as many lbs of peanuts as almonds

So

2y  = x

 

Finally......

Price per pound of each type * cost per pound of each type  = total cost

In math terms this gives us

1.50x  + 3.00y  + 1.50z  = 21 

 

AHA!!....notice, NSS, that we don't really have to do ANY MATH from this point forward......look at the third answer.....it's the only one where the number of pounds of peanuts is twice the number of pounds of almonds .....!!!!!

 

Let's verify that this is correct

1.50 (6)  + 3.00 (3)  + 1.50 (2)  =

9   + 9   +  3   =

$21  ......!!!!

 

This just proves that, sometimes, reading the problem and looking at the answers makes more sense than doing a lot of complicated math!!!

 

cool cool cool

 
CPhill  Oct 13, 2017

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