Question

5. 3x + 5y + 5z =1
x - 2y = 5
2x + 4y = 11

Answer 1

see explanation

Explanation:

Given the 3 equations

3x + 5y + 5z = 1 → (1)

x - 2y = 5 → (2)

2x + 4y = 11 → (3)

Use (2) and (3) to solve for x and y

Multiply (2) by 2

2x - 4y = 10 → (4)

Add (3) and (4) term by term

4x = 21 ( divide both sides by 4 )

x =
`(21)/(4\\)`

Substitute this value of x into (3)

2 ×
`(21)/(4\\)` + 4y = 11

`(21)/(2\\)` + 4y = 11 ( subtract
`(21)/(2\\)` from both sides )

4y =
`(1)/(2)` ( divide both sides by 4 )

y =
`(1)/(8\\)`

Substitute the values of x and y into (1) and solve for z

3 ×
`(21)/(4\\)` + 5 ×
`(1)/(8\\)` + 5z = 1

`(63)/(4)` +
`(5)/(8)` + 5z = 1

`(131)/(8)` + 5z = 1 ( subtract
`(131)/(8)` from both sides )

5z = -
`(123)/(8)` ( divide both sides by 5 )

z = -
`(123)/(40)`

Solution is

x =
`(21)/(4\\)`, y =
`(1)/(8\\)`, z = -
`(123)/(40)`