Question

How to solve $x = 4y$ and $3x - 2y = 20$ using substitution?

Answer 1

Hint: According to the question, we solve $x = 4y$ and $3x - 2y = 20$ using substitution.
So, first of all we have to substitute the value of $x$ which is $4y$ in the given equation of line which is$3x - 2y = 20$, then solve the equation and find the value of $y$ in the numerical form.
Now, we have to put the numerical value of $y$ in the given equation of line which is $x = 4y$, then solve the equation and find the value of $x$ in the numerical form.

Complete step by step solution:
Step 1: First of all we have to substitute the value of $x$ which is $4y$ in the given equation of line which is $3x - 2y = 20$
$ \Rightarrow 3\left( {4y} \right) - 2y = 20$
Step 2: Now, we have to solve the above expression which is obtained in the solution step 1 and find the value of $y$ in the numerical form.
$
   \Rightarrow 12y - 2y = 20 \\
   \Rightarrow 10y = 20 \\
   \Rightarrow y = 2 \\
 $
Step 3: Now, we have to put the numerical value of $y$ which is 2 in the given equation of line which is$x = 4y$
$
   \Rightarrow x = 4\left( 2 \right) \\
   \Rightarrow x = 8 \\
 $
Step 4: Hence, the solution for the given equation of lines are $\left( {8, - 2} \right)$.

Final solution: Hence, the solution for the given equation of lines as $x = 4y$ and $3x - 2y = 20$ is $x = 8$ and $y = 2$ or $\left( {8, - 2} \right)$.

Note:
1. It is necessary to make the given equation of line which is $3x - 2y = 20$ in terms of a single variable either $x$ or $y$ and solve for that single variable.
2. It is necessary to obtain the numerical value of any one of the variables with the help of the substitution method and then solve the numerical value of the other variable by substituting the numerical value of the first variable in the given equation of line.