Question

Solve x-y/5=6, y-z/7=8, z-x/2=10​

Answer 1

Answer:

x-y=6×5

x-y=30

y-z=8×7

= 56

z-x = 10×2

= 20

Answer 2

Answer:

1 result(s) found

{x,y,z}={8,10,14}

See steps

Step by Step Solution:

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System of Linear Equations entered :

[1] x-y/5=6

[2] y-z/7=8

[3] z-x/2=10

Equations Simplified or Rearranged :

[1] x - y/5 = 6

[2] y - z/7 = 8

[3] -x/2 + z = 10

// To remove fractions, multiply equations by their respective LCD

Multiply equation [1] by 5

Multiply equation [2] by 7

Multiply equation [3] by 2

// Equations now take the shape:

[1] 5x - y = 30

[2] 7y - z = 56

[3] -x + 2z = 20

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = 2z - 20

// Plug this in for variable x in equation [1]

[1] 5•(2?-20) - y = 30

[1] - y = 130

// Solve equation [2] for the variable z

[2] z = 7y - 56

// Plug this in for variable z in equation [1]

[1] - y = 130

[1] 69y = 690

// Solve equation [1] for the variable y

[1] 69y = 690

[1] y = 10

// By now we know this much :

x = 2z-20

y = 10

z = 7y-56

// Use the y value to solve for z

z = 7(10)-56 = 14

// Use the z value to solve for x

x = 2(14)-20 = 8

Solution :

{x,y,z} = {8,10,14}