Answer:
(a)[tex]9z+2=5[/tex]
(b)[tex]21z-11=-4[/tex]
(c)[tex]4z=2-2z[/tex]
Step-by-step explanation:
We are required to construct 3 linear equations starting with the given solution z = 1/3.
Equation 1
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 9
[tex]9z=\frac{1}{3}\times 9\\9z=3[/tex]
Rewrite 3 as 5-2
9z=5-2
Add 2 to both sides
Our first equation is: [tex]9z+2=5[/tex]
Equation 2
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 21
[tex]21z=\frac{1}{3}\times 21\\21z=7[/tex]
Rewrite 7 as 11-4
21z=11-4
Subtract 11 from both sides
Our second equation is: [tex]21z-11=-4[/tex]
Equation 3
[tex]z=\frac{1}{3}[/tex]
Multiply both sides by 6
[tex]6z=\frac{1}{3}\times 6\\6z=2[/tex]
Rewrite 6z as 4z+2z
4z+2z=2
Subtract 2z from both sides
Our third equation is: [tex]4z=2-2z[/tex]
