Linear Equation in two variables
We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.
We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.
Affiliations with Schools & Educational institutions are also welcome.
Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit
We will be happy to post videos as per your requirements also. Do write to us.
In this section we will discuss Linear Equation in two variables and different ways of solving it.
Linear equation of the form ax + by + c = 0 or ax + by = c, where a, b and c are coefficient of x and y respectively and they are real numbers, 'a' is not equal to zero (a≠0) ,'b' is not equal to zero(b ≠ 0) and x and y are variables , is called a Linear equations in two variables.
Example 1 :
2x + 3y - 4 = 0
Here, a = 2 ; b = 3 and c = -4.
Example 2 :
-x + y = 0
Here, a = -1 ; b = 1 and c = 0
A pair of linear equation in two variables is said to form a system of simultaneous linear equation.
The values of x and y are the solution of the given equation. These values satisfies the given equation.
If there is at least one solution
then the equations are consistent.
In –consistent :
If there is no solution
then the equations are in-consistent.
If the two lines are a1
x + b1
y + c1
= 0 and a2
x + b2
y + c2
= 0 then
| 1) Intersecting lines,if = consistent (one solution)
2)Coincident lines, if (infinitely many solutions)
3)Parallel lines, if = In-consistent (No solution)
For what value of k will the equations x + 2y + 7 = 0;
2x + ky + 14 = 0 represent the coincident line.
For coincident lines we have,
⇒ 1 / 2 = 2 / k = 7 / 14
⇒ 1 /2 = 2 / k
∴ k = 4
There are 4 ways to solve the linear equations.
Linear equation in two variables
• Solving linear equation by graphical method.
• Substitution method.
• Solving system of equation by elimination method
• Cross multiplication method or Cramer’s rule
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.