maheta
☼ Dependent Equation ( Parallel Lines ) : The equation of the type ax + by = c and kax + kby = kc are known as dependent equations ( or parallel lines ).
Short method to solve the pair of linear equations…
☼ System of Linear Equations :
▪ Consistent System : A system consisting of two simultaneous linear equations is said to be consistent, if it has at least one solution.
▪
☼ Cramer’s Rules ( for homogeneous system ):
If l1 : a1x + b a1y = 0
and l2 : a a2x + b a2y = 0
( Where, ai
☼ The homogeneous equation in two variables : The equation of the form ax + by = 0 ( Where, a, b are real numbers and a2 + b2
☼ Linear Equation in two variables : The equation of the form ax + by + c = 0
( Where, a, b, c are real numbers and a2 + b2
☼ Simple Equations ( Linear Equation in one variable ) : Simple equations are equations which generally have only one variable.
e.g. 2x – 3 = 7
Note : Linear Equation means the equatio…