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