Important Points and Formulas: Linear Equations In Two Variables | Mathematics (Maths) Class 9 PDF Download

Pair of Linear Equation in Two Variables

Equations → If the polynomial equates to zero, it is called equation.
4x² + 3x + 2 = 0 or 3x + 5 = 0 or 4x² + 10y = -8 Where x and y are variables 4 and 10 are coefficients of variable -8 is constant
→ A equation is called Linear equation if the highest power of variable is 1 ;
ax + b = 0;   a ≠ 0
→ A equation is called Quadratic equation if highest power of variable is 2 ;
ax² + bx + c = 0;  a ≠ 0
→ A equation is called Cubic equation if highest power of variable is 3 ;
ax³ + bx² + cx + d = 0; a ≠ 0
Linear equation in one variable is of type , ax + b = 0, a ≠ 0
Linear equation in two variable is of type ax + by + c = 0, a ≠ 0, b ≠ 0
System of linear equations in two variables are of type , a₁x + b₁y + c₁ = 0,   a₂x +b₂y + c₂ = 0
Linear equation in three variables is of type ax + by + cz + d = 0, a ≠ 0, b ≠ 0, c ≠ 0

Solutions of Linear equation 

Solution of linear equation is the value of variables which satisfy the equation.
Solution of linear equation in one variable → There is only one solution
Solution of linear equation in two variables → There are infinite number of solutions
Solution of system of linear equations in two variable → It is the value of variables which satisfy both the equations. These equations have either

1.  A unique solution such a system is called consistent. The graph consists of two intersecting lines.
2. No solution such a system is called inconsistent. The graph consists of two parallel lines.
3. Infinitely many solutions  such a system is called dependent. The graph consists of two coincident lines.

Methods of Solution of system of linear equations

1. Graphical solution
2. 
3. Cross multiplication