How to determine the variables x,y,z if y+z-x=8 and 5x=4y, x/4=z/7?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve the following system of equation sfor x, y and z

y + z - x = 8 ...(1)

5x = 4y ...(2)

x/4 = z/7 ...(3)

From (2) y = (5/4)x and from (3) z = (7/4)x

substitute these in (1)

(5/4)x + (7/4)x - x = 8

=> x(5/4 + 7/4 - 4/4) = 8

=> x*2 = 8

=> x = 4

y = 5

z = 7

The solution is x = 4, y = 5 and z = 7

imaankasana's profile pic

imaankasana | (Level 1) Honors

Posted on

y+z-x=8.......(a)

5x=4y...........(b)

x/4=z/7

or 7x=4z...........(c)

addind eq b and c

5x+7x=4y+4z

12x=4(y+z)

12x/4=y+z

3x=y+z

using value of y+z in aq a

3x -x=8

2x=8

x=4

eq b can be written as

5*4=4y

y=5

now eq c may be written as

7*4=4z

z=7

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll recall the fact that the number of variables to be determined has to be equal to the number of relations provided.

We notice that we have to determine 3 variables and the problems gives us three conditions, therefore the variables can be determined.

We'll express the y and z terms with respect to x.

5x = 4y <=> y = 5x/4

x/4 = z/7 <=> z = 7x/4

We'll replace y and z into the relation y+z-x = 8, such as:

5x/4 + 7x/4 - x = 8 <=> 12x/4 - x = 8

3x - x = 8

2x = 8 => x = 4

We'll determine y and z:

x = 4 => y = 5*4/4 => y = 5

x = 4 => z = 7*4/4 => z = 7

The variables x , y  and z are: x=4 , y=5 , z=7.

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