Question

explain the methods involved in solving of pair of linear equations in two variables.​

Answer 1

Answer:1. Elimination method 2. Substitution method 3. Cross multiplication method.

Step-by-step explanation:1. Elimination method:- in this method we have to eliminate any one variable. Ex:-

2x + 3y = 10 ( eq. 1st)

3x + 2y = 5 ( eq. 2nd)

(Trick:- multiply the coefficient of x or y from eq. 1 to eq. 2 and multiply the coefficient of x or y from eq. 2 to eq. 1)

To eliminate, we have to equal both x or both y coefficient from both equations.

We will equate the x term:-

Multiply eq. 1 with 3 and multiply eq. 2 with 2.

3( 2x +3y = 10)

2( 3x + 2y = 5)

After multiplying,

6x + 9y = 30

6x + 4y = 10

Minus eq. 2 from 1

Here, x is eliminated

5y = 20

y = 20/5

y = 4 ( eq. 3)

Put the value of eq. 3 in eq. 1 or 2

Taking eq. 1,

2x + 3y = 10 ( y = 4)

2x + 3×4 = 10

2x + 12 = 10

2x = 10 - 12

2x = -2

x = -2/2

x = -1

2. Substitution method:-

x + 8y = 19 ( eq. 1)

2x + 11y = 28 ( eq. 2)

From eq. 1,

x + 8y = 19

x = 19 - 8y (eq. 3)

Substitute the value of eq. 3 in 2

2x + 11y = 28

2(19- 8y) + 11y = 28

38- 16y+ 11y = 28

-16y + 11y = 28-38

-5y = -10

y = -10/-5

y = 2

Substitute the value of y in eq. 3

x = 19 - 8y

x = 19 - 8×2

x = 19 - 16

x = 3

3. Cross multiplication method:-

3x + y = 30 ( eq. 1)

2x + 5y = 33 ( eq. 2)

x/-33+150 = y/ -60+99= 1/15-2

x/117 = y/39 = 1/13

x/117 = 1/13

x = 117/13

x = 9

y/39 = 1/13

y = 39/13

y = 3