Question

How do you solve the system of equation \[8x-2y=13\] and \[4x+y=11\]?

Answer 1

Hint: Assume the given equations as equation (1) and (2) respectively and use the elimination method to solve the question. To eliminate the variable y, multiply equation (2) with 2 and add the obtained equation with equation (1). Cancel the variable y and find the value of x. Once the value of x is found substitute it in equation (2) to get the value of y.

Complete step-by-step solution:
Here, we have been provided with the system of equation \[8x-2y=13\] and \[4x+y=11\] and we are asked to solve it. That means we have to find the values of the variables x and y.
Now, let us use the elimination method to solve the two equations. Here, we will eliminate one of the variables and find the value of another variable. After finding the value of this variable we will substitute it in any of the two given equations and find the value of the eliminated variable.
Let us assume the given equations as equation (1) and equation (2) respectively so we have,
\[\Rightarrow 8x-2y=13\] - (1)
\[\Rightarrow 4x+y=11\] - (2)
Here, we will eliminate the variable y. So, multiplying equation (2) with 2, we get,
\[\Rightarrow 8x+2y=22\] - (3)
Adding equation (1) and (3), we get,
\[\begin{align}
  & \Rightarrow \left( 8x-2y \right)+\left( 8x+2y \right)=22+13 \\
 & \Rightarrow 16x=35 \\
\end{align}\]
Dividing both the sides with 16, we get,
\[\Rightarrow x=\dfrac{35}{16}\]
So, we have obtained the value of x, therefore substituting this value in equation (2), we get,
\[\begin{align}
  & \Rightarrow 4\times \dfrac{35}{16}+y=11 \\
 & \Rightarrow \dfrac{35}{4}+y=11 \\
 & \Rightarrow y=\dfrac{11}{1}-\dfrac{35}{4} \\
\end{align}\]
Taking L.C.M. and simplifying we get,
\[\begin{align}
  & \Rightarrow y=\dfrac{44-35}{4} \\
 & \Rightarrow y=\dfrac{9}{4} \\
\end{align}\]
Hence, the solution of the given system of equation is given as: - \[\left( x,y \right)=\left( \dfrac{35}{16},\dfrac{9}{4} \right)\].

Note: One may note that we can also apply the substitution method or the cross – multiplication method to solve the above question. But it will be suggested not to use the cross – multiplication method unless and until mentioned in the question. This is because it has a lengthy formula which must be remembered carefully or otherwise you may get the calculation wrong. Here, in the above question you can also eliminate the variable x by subtracting equations (1) and (3) and find the value of y first.