Question

How do you solve the system \[x=3y\] and \[3x-5y=12\] by substitution method?

Answer 1

Hint: We can solve this question using basic linear equation concepts. We can see that in the first equation it is directly given as x value . we will take that x value and substitute it in the second equation and find the y value. Using that y by substituting it in the first equation we will get the x value.

Complete step by step solution:
Given equations are
\[x=3y\]
\[3x-5y=12\]
We will take the first equation because it is given as x value and we need not to perform any other extra operations. We can directly substitute this into the second equation.
So the value of x we have is
\[x=3y\]
Now we have the x value so we have to substitute this in the second equation.
By substituting the x value in the second equation we will get
\[\Rightarrow 3\left( 3y \right)-5y=12\]
Now we have to simplify the equation.
Now we will remove the parenthesis in the equation.
By removing parenthesis we will get
\[\Rightarrow 9y-5y=12\]
Now we will further simplify the equation. We will get
\[\Rightarrow 4y=12\]
Now we have to simplify it for finding the value of y.
Now we have to divide with 4 on both sides of the equation.
\[\Rightarrow \dfrac{4y}{4}=\dfrac{12}{4}\]
By simplifying we will get
\[\Rightarrow y=3\]
So the y value we got is \[3\].
Now using this y value we have to find x value.
Substitute this y value in the first equation to get the value.
By substituting we will get
 \[x=3\left( 3 \right)\]
By simplifying we will get
\[\Rightarrow x=9\]

So by solving the given equations we will get x and y as \[x=9\] and \[y=3\]

Note: We can also do it by layered method. To do in the layered method we have to rewrite the equations as x and y containing terms are on LHS side and remaining on RHS side and then we can follow the process to arrive at the solution.