Pair of Linear Equations in Two Variables Test

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Pair of Linear Equations in Two Variables Test - 14

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Question 1
1 / -0

If x + y = 3 and 4x – 3y = 26 then

A
x = 5, y = 2

B
x = 5, y = -2

C
x = -5, y = -2

D
x = -5, y = 2

Solution

The given system of equation is

x + y = 3 ..……..(i)

4x – 3y = 26 ………(ii)

From (i), we get

x + y = 3

x = 3 - y

Substituting x = 3 - y in (ii), we get

4x – 3y = 26

4(3 – y) – 3y = 26

12 – 4y – 3y = 26

12 – 7y = 26

-7y = 26 – 12

-7y = 14

y = 14/-7

y = -2

Substituting y = -2 in (i), we get

x + y = 3

x + (-2) = 3

x – 2 = 3

x = 3 + 2

x = 5

Hence, the solution is x = 5, y = -2.
Question 2
1 / -0

If 10x + 3y = 75 and 6x – 5y = 11 then

A
x = 6, y = -5

B
x = -5, y = 6

C
x = 6, y = 5

D
x = -6, y = -5

Solution

The given equations are

10x + 3y = 75 ………(i)

6x – 5y = 11 ………..(ii)

Multiplying (i) by 5 and (ii) by 3, we get

50x + 15y = 375 ………(iii)

18x – 15y = 33 ………...(iv)

Adding (iii) and (iv), we get

68x = 408

x = 408/68

x = 6.

Putting x = 6 in (i), we get

10x + 3y = 75

10 x 6 + 3y = 75

60 + 3y = 75

3y = 75 – 60

3y = 15

y = 15/3 = 5

Hence, the solution is x = 6, y = 5.