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Pair of linear equations in two variables, Amisha, Vedant, Varun, Saroj…
Pair of linear equations in two variables
Consistent (independent)
If the lines are parallel, the pair of the linear equations has no solution. The pair of linear equations is inconsistent.
Thus, corresponding to each solution (x, y) of the linear equation ax + by + c = 0, there exists a point on the line representing the equation ax + by + c = 0 and vice versa.
if the lines intersect at a point, the pair of equations is consistent.The point of intersection gives the unique solution of the equations.
Consistent (dependent)
Infinite solution
Finite solution
Graphical and Algebraic method of solving
substitution method, elimination method and cross-multiplication method
Inconsistent (No solution)
A pair of linear equations will have either (a) a unique solution or (b) infinitely many solutions or (c) no solution.
A pair of linear equations is a pair of values, one for x and one for y. this pair of values is called Ordered pair.
general form for a pair of linear equatios in wo variables x and y is: a1x+b1y+c1=0
a2x+b2y+c2=0
A quadratic equation ax^2+bx+c=0
two distinct real roots, of b^2-4ac>0
Two equal roots, if b^2-4ac=0
No real roots, if b^2-4ac<0
A quadratic equation can also be solved by the method of completing the square.
A quadratic equation in the variable x is of the form ax^2+bx+c=0, where a,b,c are real numbers and a is not equal to 0
Lines parallel to each other
Coincident lines
infinite number of solutions. the pair of linear equations is consistent and dependent
lines intersecting at a single point
the pair of equation has a unique solution.
Amisha, Vedant, Varun, Saroj and Saanjh
Vedant, Amisha Varun,Saanjh and Saroj
