Question

How do you solve the system using the elimination method for $5x-3y=4$ and $3x-5y=-4$ ?

Answer 1

Hint: Here in this question we have been asked to solve the given system of equations using the elimination method for $5x-3y=4$ and $3x-5y=-4$. For answering this question, we will derive the expression for $y$ from $3x-5y=-4$ and substitute it in the other expression $5x-3y=4$ .

Complete step by step solution:
Now considering from the question we have been asked to solve the given system of equations using the elimination method for $5x-3y=4$ and $3x-5y=-4$.
For answering this question, we will derive the expression for $y$ from $3x-5y=-4$ and substitute it in the other expression $5x-3y=4$ .
The expression for $y$ from $3x-5y=-4$is given as $y=\dfrac{4+3x}{5}$ .
Now by substituting this in the other expression $5x-3y=4$ we will have $5x-3\left( \dfrac{3x+4}{5} \right)=4$
Now by simplifying this we will have
$\begin{align}
  & \Rightarrow \dfrac{25x-9x-12}{5}=4 \\
 & \Rightarrow 16x-12=20 \\
 & \Rightarrow 16x=32 \\
 & \Rightarrow x=2 \\
\end{align}$ .
Now by substituting $x=2$ in $5x-3y=4$ we will have
$\begin{align}
  & \Rightarrow 5\left( 2 \right)-3y=4 \\
 & \Rightarrow 10-3y=4 \\
 & \Rightarrow 6=3y \\
 & \Rightarrow y=2 \\
\end{align}$ .
Therefore we can conclude that the solutions of the given system of equations using the elimination method for $5x-3y=4$ and $3x-5y=-4$ is given as $\left( 2,2 \right)$ .

Note: While answering questions of this type we should be sure with our concepts that we are going to apply and simplifications that we are performing. This is a very simple and easy question and can be answered accurately in a short span of time. This question can also be answered using the graphical method. The graph of the system of equations is shown below:

The value of $y$ can also be obtained by substituting $x=2$ in $3x-5y=-4$ we will have
$\begin{align}
  & \Rightarrow 3\left( 2 \right)-5y=-4 \\
 & \Rightarrow 6-5y=-4 \\
 & \Rightarrow 10=5y \\
 & \Rightarrow y=2 \\
\end{align}$ .