CBSE Linear Equations Subject Notes

CBSE Guess > eBooks > Class X > Linear Equations by Mr. Sujeet Gaud

Linear Equations

(b) Elimination method: Following are the steps to solve the pair of linear equations by elimination method:

Step 1: First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal.

Step 2: Then add or subtract one equation from the other so that one variable gets eliminated.
(i) If you get an equation in one variable, go to Step 3.
(ii) If in Step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions.
(iii) If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.

Step 3: Solve the equation in one variable (x or y) so obtained to get its value.
Step 4: Substitute this value of x (or y) in either of the original equations to get the value of the other variable.

(c) Cross multiplication method: By cross multiplication method, the value of x and y is as follows:

when a₁b₂ – a₂b₁ ≠ 0

Algebraic Methods of Solving a Pair of Linear Equations

Equations Reducible to a Pair of Linear Equations in Two Variables:

We have several situations which can be mathematically represented by two equations that are not linear, but we change them so that they are reduced to a pair of linear equations.

1. Five years ago, Neeta was trice as old as Reeta. Ten years later, Neeta will be twice as old as Reeta, How old are Neeta and Reeta now?
2. Solve the following pair of equations graphically :

   x + 2y =5 2x +3y = -4

   Also find the points where the lines meet the x-axis.

3. Solve the following pair of linear equation graphically:

   3x-2y-1 =0 2x-3y+6=0

4. Solve the following pair of linear equations graphically:

   2x+3y=8 x +4y=9

5. Solve the following pair of linear equation graphically:

   x-2y=4 x-y =3

6. 4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750. Find the cost of 1 chair and 1 table separately.
7. Five years ago, A was thrice as old as B and 10 years hence A shall be twice as old as B. what are the present ages of A and B?
8. In a two digit number, unit's digit is twice the ten's digit. If the digits are reversed, new number is 27 more that the original number. Find the number.
9. A and B are friends and A is elder to B by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. if the ages of D and C differ by 40 years, find the age of A.
10. Ten years ago, father was twelve time as old as his son and ten years hence he will be twice as old as his son will be. Find their present ages.