Question

Construct 3 linear equation starting with qiven solution z = 1/3

Answer 1

(a)
`9z+2=5`

(b)
`21z-11=-4`

(c)
`4z=2-2z`

Explanation:

We are required to construct 3 linear equations starting with the given solution z = 1/3.

Equation 1

`z=(1)/(3)`

Multiply both sides by 9

`9z=(1)/(3)* 9\\9z=3`

Rewrite 3 as 5-2

9z=5-2

Add 2 to both sides

Our first equation is:
`9z+2=5`

Equation 2

`z=(1)/(3)`

Multiply both sides by 21

`21z=(1)/(3)* 21\\21z=7`

Rewrite 7 as 11-4

21z=11-4

Subtract 11 from both sides

Our second equation is:
`21z-11=-4`

Equation 3

`z=(1)/(3)`

Multiply both sides by 6

`6z=(1)/(3)* 6\\6z=2`

Rewrite 6z as 4z+2z

4z+2z=2

Subtract 2z from both sides

Our third equation is:
`4z=2-2z`