Question

How do you solve the equations $2x+y=7$ and $x+2y=2$?

Answer 1

Hint: Now consider the given equations to solve simultaneously we will first make the coefficient of any one variable same by multiplying the equations with appropriate scalar. Now we will subtract the equations to find the value of one of the variables. Then we will substitute it in any equation to find the value of another variable.

Complete step-by-step solution:
Now consider the given pair of equations. $2x+y=7$ and $x+2y=2$.
We know that the given equations are linear equations in two variables. Now we want to find the solution of the given equations. This means we want to find the values of x and y such that the values satisfy both the equations.
Now let $2x+y=7............\left( 1 \right)$
Now consider the second equation $x+2y=2$
Multiplying the whole equation by 2 we get, $2x+4y=4$
Let $2x+4y=4.......\left( 2 \right)$
Now subtracting equation (2) from equation (1) we get,
$\begin{align}
  & \Rightarrow 2x+y-\left( 2x+4y \right)=4-7 \\
 & \Rightarrow 2x+y-2x-4y=-3 \\
 & \Rightarrow -3y=-3 \\
\end{align}$
Now dividing the whole equation by – 3 we get the y = 1.
Hence we get the value of y = 1.
Now to find the value of x we will substitute the value of y in equation (1).
Hence we get,
$\begin{align}
  & \Rightarrow 2x+1=7 \\
 & \Rightarrow 2x=7-1 \\
 & \Rightarrow 2x=6 \\
\end{align}$
Dividing the whole equation by 2 we get x = 3.
Hence the value of x and y is 3 and 1 respectively.
Hence the solution of the given pair of linear equations is x = 3 and y = 1.

Note: Now we can also solve the linear equation by substitution method. From the second equation we can write x = 2 – 2y. And then substitute the value of x in the first equation. Hence we will get the value of y. then further substituting the value of y in any equation we get the value of x.