Question

Choose the correct option from the below given options by solving the following question:
Write four solutions for the following equation.
\[x = 4y\]
A. \[\left( {0,1} \right),\left( {4,1} \right),\left( {8,2} \right)\] and \[\left( {12,3} \right)\]
B. \[\left( {0,0} \right),\left( {4,2} \right),\left( {8,2} \right)\]and \[\left( {12,3} \right)\]
C. \[\left( {0,0} \right),\left( {4,1} \right),\left( {8,3} \right)\] and \[\left( {12,3} \right)\]
D. \[\left( {0,0} \right),\left( {4,1} \right),\left( {8,2} \right)\]and \[\left( {12,3} \right)\]

Answer 1

Hint: Take the given equation and substitute the variable with a value for four times because we were asked for four different solutions. Write the solutions in an ordered pair to get the final solution.

Complete step-by-step solution:
Given equation;
\[x = 4y\]
Taking \[y = 0\] and substituting it in the equation given, we get;
\[x = 4\left( 0 \right)\]
Now, multiplying the left-hand side, we get;
\[x = 0\]
Taking \[y = 1\] and substituting it in the equation given, we get;
\[x = 4\left( 1 \right)\]
Now, multiplying the left-hand side, we get;
\[x = 4\]
Taking \[y = 2\] and substituting it in the equation given, we get;
\[x = 4\left( 2 \right)\]
Now, multiplying the left-hand side, we get;
\[x = 8\]
Taking \[y = 3\] and substituting it in the equation given, we get;
\[x = 4\left( 3 \right)\]
Now, multiplying the left-hand side, we get;
\[x = 12\]
Now, for every value of \[y\], we have a value of \[x\].
If \[y = 0\] then \[x = 0\].
Therefore, the first solution is \[\left( {0,0} \right)\]
If \[y = 1\] then\[x = 4\].
Therefore, the second solution is \[\left( {1,4} \right)\]
If \[y = 2\] then \[x = 8\].
Therefore, the third solution is \[\left( {2,8} \right)\]
If \[y = 3\] then \[x = 12\].
Therefore, the fourth solution is \[\left( {3,12} \right)\]
Therefore, the solution is \[\left( {0,0} \right),\left( {4,1} \right),\left( {8,2} \right)\] and \[\left( {12,3} \right)\].

The correct option is D.

Note: We can also perform this solution by substituting the variable \[x\], instead of \[y\]. We are not doing it here because the options are in association with substituting \[y\], and finding the value of another variable. In order to do this in another way, take four values for \[x\], and substitute the values in the equation to get the respective values for \[y\].
Here the values of x in given particular options is 0, 4, 8, 12.
Given equation;
\[x = 4y\]
Taking \[x = 0\] and substituting it in the equation given, we get;
\[0 = 4y\]
\[ \Rightarrow y = 0\]
Taking \[x = 4\] and substituting it in the equation given, we get;
\[4 = 4y\]
$ \Rightarrow y = \dfrac{4}{4} = 1$
\[ \Rightarrow y = 1\]
Taking \[x = 8\] and substituting it in the equation given, we get;
\[8 = 4y\]
$ \Rightarrow y = \dfrac{8}{4} = 2$
\[ \Rightarrow y = 2\]
Taking \[x = 12\] and substituting it in the equation given, we get;
\[12 = 4y\]
$ \Rightarrow y = \dfrac{{12}}{4} = 3$
\[ \Rightarrow y = 3\]
Now, for every value of \[x\], we have a value of \[y\].
If \[x = 0\] then \[y = 0\].
Therefore, the first solution is \[\left( {0,0} \right)\]
If \[x = 4\] then \[y = 1\].
Therefore, the second solution is \[\left( {1,4} \right)\]
If \[x = 8\] then \[y = 2\].
Therefore, the third solution is \[\left( {2,8} \right)\]
If \[x = 12\] then \[y = 3\].
Therefore, the fourth solution is \[\left( {3,12} \right)\]
Therefore, the solution is \[\left( {0,0} \right),\left( {4,1} \right),\left( {8,2} \right)\]and \[\left( {12,3} \right)\].
The correct option is D.