Question

1. 2x + 3y =13
x-2y =-4

2. 2x+ 3y = 9
x-y=3

Solve by substitution method​

Answer 1

1) Let, Equations be :

• 2x + 3y = 13 ------(i)

• x - 2y = -4 ------(ii)

Take equation (ii) :

⇒ x - 2y = -4

⇒ x = -4 + 2y -----(iii)

Substitute the value of x in equation (i) :

⇒ 2x + 3y = 13

• x = -4 + 2y by equation (iii)

⇒ 2 × (-4 + 2y) + 3y = 13

⇒ -8 + 4y + 3y = 13

⇒ -8 + 7y = 13

⇒ 7y = 13 + 8

⇒ 7y = 21

⇒ y = 21/7

⇒ y = 3

Now,

Put value of y in any equation :

⇒ x - 2y = -4 -----(ii)

⇒ x - 2 × (3) = -4

⇒ x - 6 = -4

⇒ x = -4 + 6

⇒ x = 2

∴ Value of x is 2 and y is 3.

.

2) Let, Equations be :

• 2x + 3y = 9 -----(i)

• x - y = 3 ------(ii)

Take equation (ii) :

⇒ x - y = 3

⇒ x = 3 + y --------(iii)

Substitute the value of x in equation (ii) :

⇒ 2x + 3y = 9

• x = 3 + y by equation (iii)

⇒ 2 × (3 + y) + 3y = 9

⇒ 6 + 2y + 3y = 9

⇒ 6 + 5y = 9

⇒ 5y = 9 - 6

⇒ 5y = 3

⇒ y = 3/5

Now,

Put value of y in any equation:

⇒ x - y = 3 -----(ii)

⇒ x - 3/5 = 3

⇒ x = 3 + 3/5

⇒ x = (15 + 3)/5

⇒ x = 18/5

∴ Value of x is 18/5 and y is 3/5.

Answer 2

Answer:

Question No 1 :

2x + 3y = 13

x - 2y = - 4

Given :-

• 2x + 3y = 13
• x - 2y = - 4

To Find :-

• What is the value of x and y.

Solution :-

Given equation :

➲ 2x + 3y = 13 - - - - - - - (Equation No 1)

➲ x - 2y = - 4 - - - - - - - - (Equation No 2)

Now, from the equation no 2 we get,

↦ x - 2y = - 4

↦ x = - 4 + 2y

➦ x = - 4 + 2y

Now, we have to put the value of x in the equation no 2 we get,

↦ 2x + 3y = 13

↦ 2(- 4 + 2y) + 3y = 13

↦ - 8 + 4y + 3y = 13

↦ - 8 + 7y = 13

↦ 7y = 13 + 8

↦ 7y = 21

↦ y = 21/7

➠ y = 3

Now, by putting y = 3 in the equation no 1 we get,

↦ 2x + 3y = 13

↦ 2x + 3(3) = 13

↦ 2x + 3 × 3 = 13

↦ 2x + 9 = 13

↦ 2x = 13 - 9

↦ 2x = 4

↦ x = 4/2

➠x = 2

∴ The value of x is 2 and the value of y is 3.

______________________________

Question No 2 :

2x + 3y = 9

x - y = 3

Given :

• 2x + 3y = 9
• x - y = 3

To Find :

• What is the value of x and y.

Solution :-

Given equation :

➲ 2x + 3y = 9 - - - - - - - - (Equation No 1)

➲ x - y = 3 - - - - - - - - - - (Equation No 2)

Now, from the equation no 2 we get,

↦ x - y = 3

↦ x = 3 + y

➠ x = 3 + y

Now, by putting the value of x in the equation no 1 we get,

↦ 2x + 3y = 9

↦ 2(3 + y) + 3y = 9

↦ 2(3) + 2(y) + 3y = 9

↦ 6 + 2y + 3y = 9

↦ 6 + 5y = 9

↦ 5y = 9 - 6

↦ 5y = 3

↦ y = 3/5

➠ y = 3/5

Now, by putting the value of y = 3/5 in the equation no 1 we get,

↦ 2x + 3y = 9

↦ 2x + 3(3/5) = 9

↦ 2x + 9/5 = 9

↦ 2x = 9 - 9/5

↦ 2x = 45 - 9/5

↦ 2x = 36/5

↦ x = 36/5 × 1/2

↦ x = 18/5 × 1

➠ x = 18/5

∴ The value of x is 18/5 and the value of y is 3/5.