Question

How do you solve the system $2x-3y=-24$ and $x+6y=18$ using substitution.

Answer 1

Hint: Now to solve the equation by substitution method we will first consider the equation $x+6y=18$ and then arrange the terms to write the equation as $x=18-6y$ . Now we will substitute the value of x in the second equation and hence find the value of y. Now we will again substitute the value of y in the any equation and find the value of x. Hence we have the solution of the given equation.

Complete step-by-step answer:
Now consider the linear equations $2x-3y=-24$ and $x+6y=18$.
Now we want to find the solution of the equation by using a substitution method.
To do so first consider the equation $x+6y=18$ . Now transposing 6y on RHS we get,
$x=18-6y$
Now we will substitute the value of x in the equation $2x-3y=-24$ Hence we get,
$\Rightarrow 2\left( 18-6y \right)-3y=-24$
Now opening the bracket we get,
$\begin{align}
  & \Rightarrow 36-12y-3y=-24 \\
 & \Rightarrow 36-15y=-24 \\
\end{align}$
Now transposing 24 on LHS and 15y on RHS we get,
$\begin{align}
  & \Rightarrow 36+24=15y \\
 & \Rightarrow 60=15y \\
\end{align}$
Hence dividing the whole equation by 15 we get.
$y=4$.
Now substituting the value of y in equation $x=18-6y$ we get x = - 6.
Hence the solution of the equation is x = - 6 and y = 4.

Note: Now note that when we are using substitution method we can express x in terms of y or y in terms of x. Here to avoid complications of fractions we have taken x in terms of y. Now remember when we are substituting the value of x always substitute in another equation which has not been used to write x in terms of y or y in terms of x.