Question

How do you solve the system \[y=2x+1,y=3x-7\]?

Answer 1

Hint: From the question given, we have been asked to solve the system \[y=2x+1,y=3x-7\]. We can solve the given question by understanding the question correctly and applying some basic transformations to the given system of equations. Then we have to simplify further to get the given system of equations solved.

Complete step-by-step answer:
From the question given, we have been given system of equations \[y=2x+1,y=3x-7\]
We can clearly observe that, in the given system of equations, the left hand side of both the equations are equal, that is \[y\].
So, we can equal the right hand side of the given system of equations to get the equation solved.
By equating the right hand sides of the both the equations, we get \[\Rightarrow 2x+1=3x-7\]
Now, shift \[2x\] from the left hand side of the equation to the right hand side of the equation. By shifting \[2x\] from the left hand side of the equation to the right hand side of the equation, we get
\[\Rightarrow 1=3x-2x-7\]
\[\Rightarrow 1=x-7\]
Simplify further the above equation to get the values of the variables. By simplifying further we get,
\[\begin{align}
  & \Rightarrow x=1+7 \\
 & \Rightarrow x=8 \\
\end{align}\]
Now, substitute for \[x\] in any of those two equations to get the value of \[y\].
Therefore,
\[\begin{align}
  & \Rightarrow y=2x+1 \\
 & \Rightarrow y=2\left( 8 \right)+1 \\
 & \Rightarrow y=16+1 \\
 & \Rightarrow y=17 \\
\end{align}\]
Hence, \[x=8,y=17\]
Hence, the given systems of equations are solved.

Note: We should be well aware of solving the given system of equations using some basic transformations to the given question. After getting the value of one variable, we should use it and get the value of another variable. Also, we should be very careful while doing the calculation part. It will be efficient if we verify the answer before finalizing it. In this case verification is done by substituting the value of $x$ in both the equations and observing if the value of $y$ is the same. For $y=2x+1$ if we substitute $x=8$ we have $y=17$ we need to check for $y=3x-7$ if we substitute $x=8$ we have
$\begin{align}
  & y=3\left( 8 \right)-7 \\
 & \Rightarrow y=24-7 \\
 & \Rightarrow y=17 \\
\end{align}$