Question

What is the solution of the system of equations $2x+3y=7,x+y=3$?

Answer 1

Hint: The given above equations are linear equations in two variables. An equation for a straight line is called a linear equation. The above equation is a linear equation of two variables. Any equation which can be put in the form $ax+by+c=0$, where a, b, and c are real numbers, and a and b are not zero, is called a linear equation in two variables.

Complete step by step solution:
The given two equations are:
$\Rightarrow 2x+3y=7$ and
$\Rightarrow x+y=3$
Here we have to find the value to x and y such that they satisfy the both above equations.
To find the value of x and y, we will use elimination method.
The equations are:
$\Rightarrow 2x+3y=7.......1$
$\Rightarrow x+y=3.........2$
To eliminate these equation we have make a coefficient of any one variable same, so for this we will multiply the equation 2 by 2, then we get,
$\Rightarrow 2x+3y=7.......(3)$
$\Rightarrow 2x+2y=6............(4)$
Now by subtraction both the equation (3) and (4), then we get
$\Rightarrow y=1$
Now, put this value of y in equation (1), then we get the value of x from equation (1)
$\Rightarrow 2x+3(1)=7$
Now subtraction $3$ from both sides of the equation, then we get
$\begin{align}
  & \Rightarrow 2x+3-3=7-3 \\
 & \Rightarrow 2x=4 \\
 & \Rightarrow x=2 \\
\end{align}$
Hence we get the value of x and y which are$\left( 2,1 \right)$ .

Note: In any equation the thing is to be remembered is that if we multiply any equation with any constant then the value of the equation does not change. To solve linear equations with two variables we used elimination method, if we have three variables linear equation then we will use matrix method.