Question

Write four solutions for the following equation \[x=4y\].
A. \[\text{(0,1) (4,1) (8,2) (12,3)}\]
B. \[\text{(0,0) (4,1) (8,2) (12,3)}\]
C. \[\text{(0,0) (4,1) (8,3) (12,3)}\]
D. \[\text{(0,0) (4,1) (8,3) (12,3)}\]

Answer 1

Hint: To find the right solution, put the value of each \[(x,y)\] in the given equation and check if it satisfies the equation.

Complete step-by-step answer:
A. Given values are
\[\text{(0,1) (4,1) (8,2) (12,3)}\]
Equation \[x=4y\] ….. 1
Put \[x=0\] in \[x=4y\]
Where \[x=0\]
\[y=1\]
L.H.S \[x=0\]
R.H.S \[4y=4\times 1=4\]
Here \[L.H.S\ne R.H.S.\]
As one out of values don’t satisfy the equation, (A) is wrong.

B. Given values
\[\text{(0,0) (4,1) (8,2) (12,3)}\]
Put \[x=0\]in \[x=4y\]
L.H.S \[=x=0\]
R.H.S \[=4y=4\times 0=0\]
Here \[L.H.S=R.H.S.\]
Put \[(4,2)\]in
L.H.S \[=x=4\]
R.H.S \[=4y=4\times 2=8\]
Here \[L.H.S\ne R.H.S.\]
So, (B) part is not the solution.

C. Given values
\[\text{(0,0) (4,1) (8,3) (12,3)}\]
Put \[\text{(0,0)}\]in \[x=4y\]
L.H.S \[=x=0\]
R.H.S \[=4y=4\times 0=0\]
Here \[L.H.S=R.H.S.\]
Put \[(4,1)\]in \[x=4y\]
L.H.S \[=x=4\]
R.H.S \[=4y=4\times 1=4\]
Here \[L.H.S=R.H.S.\]
Put \[(8,3)\]in \[x=4y\]
L.H.S \[=x=8\]
R.H.S \[=4y=4\times 3=12\]
\[L.H.S\ne R.H.S.\]
So, \[(8,3)\]does not satisfy the equation and (C) is therefore not the solution.

D. Given values
\[\text{(0,0) (4,1) (8,3) (12,3)}\]
Put\[\text{(0,0)}\] in \[x=4y\]
\[LHS=RHS=0\]
Put \[(4,1)\]in \[x=4y\]
L.H.S \[=x=4\]
R.H.S \[=4y=4\times 1=4\]
Here \[L.H.S=R.H.S.\]
Put \[(8,2)\]in \[x=4y\]
L.H.S \[=x=8\]
R.H.S \[=4y=4\times 2=8\]
Here \[L.H.S=R.H.S.\]
Put \[(12,3)\]in \[x=4y\]
L.H.S \[=x=12\]
R.H.S \[=4y=4\times 3=12\]
\[L.H.S=R.H.S.\]
Since all 4 values satisfy the equation, D is the right answer.

Note: Even if one value is not satisfying the equation, the solution is not correct.
Do not check further points if you get the first point as incorrect.