**Hi friends, welcome on Maths Master, here you will learn how to solve linear equations in two variables by using Eliminations and substitution methods.**

**Meaning of Linear Equations in Two Variables:**

An equation which contains two variables and the degree of each term containing variable is one, is called a linear equation in two variables. ax + by + c = 0 is the general form of a linear equation in two variables;

a, b, c are real numbers and a, b are not equal to zero at the same time.

Ex. 3x – 4y + 12 = 0 is the general form of equation 3x = 4y – 12

**Methods of Solving Equations in Two Variables:**

1. Substitution Method

2. Elimination Method

3. Determinant Method OR Cramer’s Rule

4. Graphical Method

In Practice set 1.1 we learn to solve examples by using elimination and substitution method.

other method we shall learn in further practice sets of this chapter.

**Elimination Method**

In the elimination method you either **add or subtract the equations to get an equation in one variable**.

When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

Learn elimination method thoroughly, because it will will help you to solve any other questions also from this chapter.

Let’s see some examples:

(1) 5x – 3y = 8; 3x + y = 2

Sol.:

5x -3y =8 …………………(1)

3x + y = 2 ………………..(2)

Multiply equation (2) by 3

9x + 3y = 6 ………………….(3)

Adding equations (1) and (3)

5x – 3y =8

9x + 3y =6

…………………………….

14 x = 14

x= 14/14

x = 1

Put x=1 in equation (2)

3 X 1 +y = 2

3 +y = 2

y = 2-3

y = -1

Ans. : x=1 and y =-1

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**Substitution Method**

**The method of substitution involves three steps****:**

1.Solve one equation for one of the variables.

2.Substitute (plug-in) this expression into the other equation and solve.

3.Resubstitute the value into the original equation to find the corresponding variable.

If in exam it is mention that use substitution method, then you have to use, either you can use elimination method only.

(1) 5x – 3y = 8; 3x + y = 2

Sol.:

5x -3y =8 …………………(1)

3x + y = 2 ………………..(2)

3x + y = 2

y = 2-3x ……………………(3)

Put the value of y in equation (1)

5x – 3( 2-3x) = 8

5x- 6 + 9x =8

14x -6 = 8

14x =8+6

14x=14

x= 14/14

x = 1

Put x=1 in equation (3)

y = 2-3 X 1

y = 2-3

\therefore y=-1

Ans. : x=1 and y =-1

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**Practice Set 1.1**

Click Here For Video Solution

- Solve the following simultaneous equations.

(1) 3a + 5b = 26; a + 5b = 22 (2) x + 7y = 10; 3x – 2y = 7

(3) 2x – 3y = 9; 2x + y = 13 (4) 5m – 3n = 19; m – 6n = -7

(5) 5x + 2y = -3; x + 5y = 4 (6) 1/3x + y = 10/3 ; 2x+ 1/4y=11/4

(7) 99x + 101y = 499; 101x + 99y = 501

(8) 49x – 57y = 172; 57x – 49y = 252

I have solved above example in this video by using elimination method, so now watch the video.If you will watch this video, there will be no further any doubts. After learning this chapter you can play quiz based on this chapter.

Click Here For Video Solution

## More Questions for Practice

- (i) x + y = 4 ; 2x – 5y = 1 (ii) 2x + y = 5; 3x-y = 5

(iii) 3x – 5y=16; x-3y=8 (iv) 2y – x=0; 10x + 15y = 105

(v) 2x + 3y+4 = 0; x- 5y = 11 (vi) 2x – 7y = 7; 3x + y = 22 - (vii) 2x + y = 5 ; 3x – y = 5 (viii) x – 2y = -1 ; 2x- y = 7
- (ix) x + y = 11 ; 2x – 3y = 7 (x) 2x + y = -2 ; 3x – y = 7
- (xi) 2x – y = 5 ; 3x + 2y = 11 (xii) x – 2y = -2 ; x + 2y = 10

## Click below to play Quiz

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