Question

Solve by elimination method:
$\begin{align}
  & 3x+4y=-25; \\
 & 2x-3y=6 \\
\end{align}$

Answer 1

Hint: It is given as we have to solve the given system of simultaneous equations by elimination method so multiply the first equation by 3 and multiply the second equation by 2 then add these equations. After addition, you will find that y is eliminated and you will be left with x and then simplify and get the value of x and then substitute this value of x in the second equation. It will give you the value of y.

Complete step-by-step answer:
The two simultaneous equations given in the question are:
$\begin{align}
  & 3x+4y=-25..........Eq.(1) \\
 & 2x-3y=6...............Eq.(2) \\
\end{align}$
Multiplying eq. (1) by 3 and multiplying eq. (2) by 4 and then we are going to add these equations.
$\begin{align}
  \left( 3x+4y=-25 \right)\times 3 & \\
  \dfrac{+\left( 2x-3y=6 \right)\times 4}{\left( 9+8 \right)x=-75+24} & \\
\end{align}$
Simplifying the above equation we get,
$\begin{align}
  & 17x=-51 \\
 & \Rightarrow x=-3 \\
\end{align}$
Substituting this value of x in eq. (1) we get,
$\begin{align}
  & 3\left( -3 \right)+4y=-25 \\
 & \Rightarrow -9+4y=-25 \\
 & \Rightarrow 4y=-16 \\
 & \Rightarrow y=-4 \\
\end{align}$
From the above solving equations by elimination method we have found the value of x = -3 and y = -4.
Hence, the value of x = -3 and y = -4 in the given simultaneous equation.

Note: We can solve the given system of simultaneous equations other than using elimination methods.
The method is a substitution method.
The given system of simultaneous equations is:
$\begin{align}
  & 3x+4y=-25..........Eq.(1) \\
 & 2x-3y=6...............Eq.(2) \\
\end{align}$
From eq. (1), writing x in terms of y we get,
$\begin{align}
  & 3x+4y=-25 \\
 & \Rightarrow 3x=-25-4y \\
 & \Rightarrow x=\dfrac{-25-4y}{3} \\
\end{align}$
Substituting this value of x in the eq. (1) we get,
$\begin{align}
  & 2\left( \dfrac{-25-4y}{3} \right)-3y=6 \\
 & \Rightarrow -50-8y-9y=18 \\
 & \Rightarrow -17y=68 \\
 & \Rightarrow y=-4 \\
\end{align}$
Plugging this value of y in the expression which is x in terms of y we get,
$\begin{align}
  & x=\dfrac{-25-4y}{3} \\
 & \Rightarrow x=\dfrac{-25-4\left( -4 \right)}{3} \\
 & \Rightarrow x=\dfrac{-25+16}{3} \\
 & \Rightarrow x=\dfrac{-9}{3}=-3 \\
\end{align}$
From the above calculations, we are getting the value of x = -3 and y = -4 which is the same as that we have got the solution part of the question.