Question

How do you solve the equation $2x-3y=21$ and $5x-2y=25$?

Answer 1

Hint: Now we are given a linear equation in two variables. To find the solution of the equation we will first try to eliminate y. To do so, we will multiply each equation with an appropriate number such that the coefficients of y in both equations are the same. Now we will subtract the two equations and find the value of x. now substituting the value of x in any given equation we find the value of y.

Complete step by step solution:
Now we are given with two linear equations in x and y.
Now to solve the equation we will first have to form a linear equation in one variable out of them.
To do so we will eliminate a variable.
Let us say we eliminate the variable y.
To do so we will first have to make coefficients of y same for both the equations.
Hence consider the equation $2x-3y=21$
Now multiplying the whole equation by 2 we get,
$\Rightarrow 4x-6y=42..........\left( 1 \right)$
Now consider the equation $5x-2y=25$
Multiplying the whole equation by 3 we get
$\Rightarrow 15x-6y=75...................\left( 2 \right)$
Subtracting equation (2) from equation (1) we get,
$\begin{align}
  & \Rightarrow 15x-6y-\left( 4x-6y \right)=75-42 \\
 & \Rightarrow 15x-6y-4x+6y=33 \\
 & \Rightarrow 11x=33 \\
 & \Rightarrow x=3 \\
\end{align}$
Hence we get the value of x = 3.
Now substituting the value of x in equation (1) we get,
$\begin{align}
  & \Rightarrow 15\left( 3 \right)-6y=75 \\
 & \Rightarrow 45-6y=75 \\
 & \Rightarrow 45-75=6y \\
 & \Rightarrow -30=6y \\
 & \Rightarrow y=-5 \\
\end{align}$
Hence the value of y is – 5.
Hence the solution of the given equation is x = 3 and y = - 5.

Note: Now note that we can solve linear equations by method of substitution also. In this method we will consider one of the two equations and express one variable in terms of another. Let us say we express y in terms of x. Now we will substitute the value of y in the other equation. Hence we get the value of x. Now substituting this value of x in the any equation we will get the value of y.