Question

How do you solve the system $3x+6y=30$ and $x+6y=20$?

Answer 1

Hint: To solve the given system of equations we will use the elimination method. We eliminate one of the variables from equations by adding or subtracting the equations and find the value of the other variable. Then substitute the value in one of the equations to get the value of the variable.

Complete step-by-step solution:
We have been given the system $3x+6y=30$ and $x+6y=20$
We have to solve the given equations.
Now, to solve the equations we use the elimination method. First we will subtract both equations to eliminate the variable y from the equations.
We have
$3x+6y=30........(i)$
$x+6y=20......(ii)$
Now, let us subtract equation (ii) from equation (i) then we will get
$\begin{align}
  & 3x+6y=30 \\
 & \underline{x+6y=20} \\
 & 2x=10 \\
\end{align}$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow x=\dfrac{10}{2} \\
 & \Rightarrow x=5 \\
\end{align}$
Now, substituting the value of x in equation (i) we will get
$\Rightarrow 3\times 5+6y=30$
Now, simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow 15+6y=30 \\
 & \Rightarrow 6y=30-15 \\
 & \Rightarrow y=\dfrac{15}{6} \\
 & \Rightarrow y=\dfrac{5}{2} \\
\end{align}$
Hence on solving the given system we get the values of x and y as 5 and $\dfrac{5}{2}$ respectively.

Note: Alternatively students can use a substitution method also to solve the system of equations. Here we use the elimination method to solve the equations. The point to be remembered is that in the elimination method the coefficients of the variable which we want to eliminate are equal in both the equations before adding or subtracting the equations. If coefficients are not equal then we have to multiply or divide the equation by any suitable number.