Question

The equation which cannot be solved in integers is

• A. $5y–3=–18$
• B. $3x–9=0$
• C. $3z+8=3+z$
• D. $9y+8=4y–7$

Answer 1

The correct option is C

$3z+8=3+z$

Step 1: Explanation for correct option.

Solve Option (C)

$$\begin{gathered} 3z+8=3+z \\ 3z=3+z–8 \\ 3z=z–5 \\ 3z–z=-5 \\ 2z=–5 \\ z=\frac{-5}{2}(Isnotaninteger) \end{gathered}$$

Step 2: Explanation for incorrect option.

Solve Option (A)

$$\begin{gathered} 5y=-18+3 \\ 5y=–15 \\ y=\frac{-15}{5} \\ y=-3\left(Integer\right) \end{gathered}$$

Solve Option (B)

$$\begin{gathered} 3x–9=0 \\ 3x=9 \\ x=\frac{9}{3} \\ x=3\left(Integer\right) \end{gathered}$$

Solve Option (D)

$$\begin{gathered} 9y+8=4y–7 \\ 9y=4y–7–8 \\ 9y=4y–15 \\ 9y–4y=–15 \\ 5y=-15 \\ y=\frac{-15}{5} \\ y=-3\left(Integer\right) \end{gathered}$$

Hence, the correct option is C.