Question

How do you solve the system of linear equations $2x-3y=3$ and $5x-4y=4$ ?

Answer 1

Hint: Now to solve the system of linear equations we will use the algebraic approach. First consider the given equations. Now we will multiply the equation $2x-3y=3$ by 5 and the equation $5x-4y=4$ by 2. Now we will subtract the two obtained equations such that we get a linear equation in y. Now we will solve this linear equation to find the value of 6. Now substituting y in any equation we will get the value of x. Hence we have the solution of the given equation.

Complete step by step solution:
We are given with linear equations in two variables. To find the solution of the given equations we will use the algebraic approach.
Now consider the equation $2x-3y=3$
Multiplying the whole equation by 5 we get
$\Rightarrow 10x-15y=15............\left( 1 \right)$
Now consider the equation $5x-4y=4$
Multiplying the equation with 2 we get,
$\Rightarrow 10x-8y=8.....\left( 2 \right)$
Now subtracting equation (1) from equation (2) we get,
$\begin{align}
  & \Rightarrow 10x-8y-10x+15y=8-15 \\
 & \Rightarrow 7y=-7 \\
 & \Rightarrow y=-1 \\
\end{align}$
Hence we get the value of y = -1.
Now substituting the value of y in the equation (1) we get,
$\begin{align}
  & \Rightarrow 10x-15\left( -1 \right)=15 \\
 & \Rightarrow 10x=15+15 \\
 & \Rightarrow 10x=30 \\
 & \Rightarrow x=3 \\
\end{align}$

Hence the value of x = 3 and the value of y = - 1.

Note: Now note that when we have the solution to the linear equations always check the solution by substituting the values in the equations. Hence substitute the values of x and y in both the equations and check if both the equation holds. Also note that the system of linear equations can also have no solution or infinite solution.