Question

Class 10

Mathematics

Chapter 3 - Pair of linear equation in two variables

Formulas Needed

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Answer 1

Step-by-step explanation:

Pair of linear equations in two variables:-

The general form of a linear equations in two variables is ax+by+c=0

It has infinitely number of solutions.

Types:-

If a1 x+b1 y +c1 = 0 and a2x+b2y+c2=0 are the pair of linear equations then

• If a1/a2≠b1/b2 ≠c1/c2 then they are consistent and independent lines.

• The graph of the above lines is intersecting lines with an unique solution.

• If a1/a2 = b1/b2 ≠c1/c2 then they are inconsistent lines .

• The graph of the above lines is parallel lines with no solution.

• If a1/a2 = b1/b2 = c1/c2 then they are Consistent and dependent lines.

• The graph of the above lines is coincident lines with infinitely number of many solutions.

Solutions:-

• Intersecting lines -1

• Parallel lines -0

• Coincident lines -infinite

Solving methods:-

• Elimination method

• Substitution method

• cross multiplication method

• reduced to Linear equations method.