Question

Write any two solutions for the equation \[x - 2y = 5\] .

Answer 1

Hint: Substitute the value of variable as zero to find the solution.
In this question we are given with an algebraic equation and the equation contains two variables \[x\] and \[y\] , to find the solution of the equation substitute the value of the variable as zero and then we will get one solution of the equation and again substitute the value of the other variable as zero to find the second solution of the equation.

Complete step-by-step answer:
Given the algebraic equation whose solution is to be find is \[x - 2y = 5\]
Here in the given equation we can see the equation contains two variables \[x\] and \[y\]
Now to find the first solution of the equation, let’s substitute the value of the variable \[x\] as \[x = 0\] in the equation, hence by substituting we get
 \[
  x - 2y = 5 \\
   \Rightarrow 0 - 2y = 5 \;
 \]
By solving the equation, we get
 \[
   - 2y = 5 \\
   \Rightarrow y = - \dfrac{5}{2} \;
 \]
Hence one of the solution of the above equation is \[\left( {0, - \dfrac{5}{2}} \right)\]
Now to find the second solution of the given equation, let’s substitute the value of the variable \[y\] as \[y = 0\] in the equation, hence by substituting we get
 \[
  x - 2y = 5 \\
   \Rightarrow x - \left( {2 \times 0} \right) = 5 \;
 \]
By solving, we get
 \[
  x - 0 = 5 \\
   \Rightarrow x = 5 \;
 \]
Hence the second solution of the above equation is \[\left( {5,0} \right)\]
Therefore the two solutions for the equation \[x - 2y = 5\] are \[\left( {0, - \dfrac{5}{2}} \right)\] and \[\left( {5,0} \right)\] .
So, the correct answer is “ \[\left( {0, - \dfrac{5}{2}} \right)\] and \[\left( {5,0} \right)\] .”.

Note: Solution of the equation gives all the values of the equation which are when substituted in the original equations they satisfy the values. In this question we got two solutions for the equation \[x - 2y = 5\] as \[\left( {0, - \dfrac{5}{2}} \right)\] and \[\left( {5,0} \right)\] , now if we substitute these values in the equation then the equation will be satisfied.
To verify:
For \[\left( {0, - \dfrac{5}{2}} \right)\]
 \[
  \left( 0 \right) - 2\left( { - \dfrac{5}{2}} \right) = 5 \\
   \Rightarrow 0 + 5 = 5 \\
   \Rightarrow 5 = 5 \;
 \]
Hence, Verified.
For $\left( {5,0} \right)$
 \[
  5 - 2\left( 0 \right) = 5 \\
   \Rightarrow 5 - 0 = 5 \\
   \Rightarrow 5 = 5 \;
 \]
Hence, Verified.