Question

1. Solve the system of equations by using the substitution

method.
x + 3y = 6
2x + 5y = 9
2. Solve the system of equations by using the addition
method.
5x - 4y = -5
10x + 5y = 55
3. Solve the system

Answer 1

1. Solution set = { (-3, 3) }

2. Solution set = { (3, 5) }

Explanation:

Answer 1. x + 3y = 6

⇒ x = 6 - 3y ...(1)

2x + 5y = 9 ...(2)

Substituting (1) in (2):-

2x + 5y = 9

⇒ 2(6 - 3y) + 5y = 9

⇒ 12 - 6y + 5y = 9

⇒ 12 - 1y = 9

⇒ -1y = 9 - 12

= -3

⇒ y = -3/-1

= 3

⇒ ∴ y = 3

Now, substituting y = 3 in (1):-

x = 6 - 3y

⇒ x = 6 - 3(3)

= 6 - 9

= -3

⇒ ∴ x = -3

Answer:- ∴ The solution set = { (-3, 3) }

Answer 2. 5x - 4y = -5 ...(1)

10x + 5y = 55 ...(2)

Multiplying equ. (1) by 5 and (2) by 4.

Now, using elimination method:-

25x - 20y = -25

40x + 20y = 220

65x = 195

⇒ 65x = 195

⇒ x = 195/65

= 3

⇒ ∴ x = 3

Now, substituting x = 3 in equ. (1):-

5x - 4y = -5

⇒ 5(3) - 4y = -5

⇒ 15 - 4y = -5

⇒ -4y = -5 - 15

= -20

⇒ y = -20/-4

= 5

⇒ ∴ y = 5

Answer:- ∴ The solution set = { (3, 5) }