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Find x, if: 3x=5y=8z and x-y-z=-3

 Jun 26, 2020
 #1
avatar+28021 
+1

multiply the equation by 5  to get

 

5x - 5y - 5z = -15         now since   5y = 3x

5x - 3x - 5z = -15          multiply THIS equation by 1.6

8x -4.8x - 8z = -24        now since 8z = 3x

8x - 4.8x -3x = -24

x = -120

 Jun 26, 2020
 #2
avatar+8352 
0

It is good if we can express everything in terms of x. Because it will become a linear equation in one variable. 

 

In fact, we can. Manipulating the first equation:

 

3x = 5y

y = 3x/5 = 0.6 x

 

3x = 8z

z = 3x/8 = 0.375 x

 

Then, we plug these into the equation:

 

\(x-0.6x-0.375x=-3\)

 

We simplify the left hand side:

\(0.025x = -3\)

Changing that 0.025 into a fraction gives

\(\dfrac x{40} =-3\\ \)

We multiply 40 to both sides to get

x = -120.

 Jun 26, 2020

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