Question

se by using the
of
Find the solution set by using
mechod
method
of elimination
Substitution
x + 8y = 15
34. y .o
+ 8y = 15
by
a
رن) -
3- y =
3a = 9
= 0
(ii)
x = y
3​

Answer 1

Step-by-step explanation:

(i) By elimination method:

x + y = 5————-(1)

2x – 3y = 4 ————(2)

Multiplying equation (1) by 2,

2x + 2y = 10 —————-(3)

Subtracting equation (2) from equation (3),

5y = 6

y = 6/5 ————-(4)

Substituting the value in equation (1),

x = 5 – 6/5 = 19/5

x = 19/5 , y = 6/5

By substitution method:

From equation (1),

x = 5 – y ————-(5)

Put the value of x in (2)

2(5-y) – 3y = 4

-5y = – 6

y = 6/5

Substituting the value in equation (5)

x = 5 – 6/5 = 19/5

x = 19/5 ; y = 6/5

(ii) By elimination method:

3x + 4y = 10 ———-(1)

2x – 2y = 2———(2)

Multiplying equation (2) by 2,

4x – 4y = 4 ————(3)

Adding equation (1) and (3),

7x = 14

x = 2 —————(4)

Substituting in equation (1),

6 + 4y = 10

4y = 4

y = 1

Thus, x = 2, y = 1

By substitution method:

From equation (2),

x = 1 + y ———- (5)

Put the value of x in equation (1),

3(1+y)+4y = 10

7y = 7

y = 1

Substituting the value in equation (5),

x = 1+1=2

x = 2, y = 1

(iii)By elimination method:

3x – 5y – 4 = 0 ————(1)

9x = 2y + 7

9x – 2y – 7 = 0 ————–(2)

Multiplying equation (1) by 3,

9x – 15y – 12 = 0 ————(3)

Subtracting equation (3) from equation (2),

13y = -5

y = -5/13

Substituting in equation (1),

3x + 25/13 – 4 = 0

3x = 27/13

x = 9/13

x = 9/13 ; y = -5/13

By substitution method:

From equation (1),

x = 5y+4/3 ————–(5)

Putting this value in equation (2),

9(5y+4/3) – 2y – 7 = 0

13y = -5

y = ‑5/13

Substituting the value in equation (5),

x = [5(-5/13)+4]/3 = 9/13

Thus, x = 9/13 and y = ‑5/13

(iv) By elimination method

x/2 + 2y/3 = -1

3x + 4y = -6 ———–(1)

x – y/3 = 3

3x – y = 9 —————-(2)

Subtracting equation (2) from equation (1),

5y = -15

y = -3 —————(3)

Substituting this value in equation (1),

3x – 12 = -6

3x = 6

x = 2

Hence, x = 2, y = −3

By substitution method:

From equation (2),

x = y+9/3———– (5)

Putting this value in equation (1),

3(y+9/3) + 4y = -6

5y = -15

y = -3

Substituting the value in equation (5),

x = -3+9/3 = 2

∴ x = 2, y = −3