Question

How do you solve the system of linear equation $x-7y=21$ and $2x-7y=28$

Answer 1

Hint: Now to solve the equation we will first multiply the equation $x-7y=21$ with 2. Now we will subtract the obtained equation from equation $2x-7y=28$ . Hence we will get a linear equation in terms of y. We will solve it to find y and then substitute the value of y in any equation to find the value of x. Hence we have the solution to the given equation.

Complete step by step solution:
Now we are given a linear equation in two variables.
To s=find the solution of the given equations we must find the value of x and y such that the values satisfy both the equation simultaneously.
To do so we will try to eliminate one of the variables and form a linear equation in one variable.
Now let us say we want to eliminate x from the equations.
Then we must make the coefficient of x same form both the equations. Hence we can either divide the second equation by 2 or multiply the first equation by 2.
To avoid fractions let us multiply the first equation by 2 hence we get $2x-14y=42$
Now we will consider the two equations $2x-14y=42$ and $2x-7y=28$ .
Now to eliminate x we can see that we must subtract the equations.
Hence we get
$\begin{align}
  & \Rightarrow 2x-14y-\left( 2x-7y \right)=42-28 \\
 & \Rightarrow 2x-14y-2x+7y=14 \\
 & \Rightarrow -7y=14 \\
 & \Rightarrow y=-2 \\
\end{align}$
Now we have the y = - 2.
To find x we will substitute the value of y in any of the equations.
Let us say we substitute y = - 2 in the equation $x-7y=21$
Hence we have,
$\begin{align}
  & \Rightarrow x-7\left( -2 \right)=21 \\
 & \Rightarrow x+14=21 \\
 & \Rightarrow x=21-14 \\
 & \Rightarrow x=7 \\
\end{align}$

Hence the value of x = 7 and y = -2.

Note: Now note that when we have two variables we can eliminate one variable by various methods. Here we have used algebraic operations to eliminate x. we can also do the same with y too. Now we can also use a method of substitution to eliminate variables. In this we express one variable in terms of another and substitute the value in the other equation. Hence we again get an equation in one variable.