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

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 | (Level 1) Honors

Posted on

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

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

x/4=z/7

or 7x=4z...........(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 | 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.