Pair of Linear Equations in Two Variables Test - 15

y = 9 and y = -7 are lines parallel to X-axis, thus these parallel lines and hence no solution

Let,

Cost of 1 pencil = x

Cost of 1 pen = y

A/Q,

5x + 7y = 50  ……..(i)

7x + 5y = 46 ………(ii)

Multiplying (i) by 5 and (ii) by 7, we get

25x + 35y = 250  ………(iii)

49x + 35y = 322  ………...(iv)

Subtracting (iv) from (iii), we get

25x – 49x = 250 – 322

-24x = -72

x = −72/−24

x = 3

Putting x = 3 in (i), we get

5x + 7y = 50

5 x 3 + 7y = 50

15 + 7y = 50

7y = 50 – 15

7y = 35

y = 35/7

y = 5

Hence, the solution is x = 3, y = 5.

Cost of 2 pencil and 3 pens = 6 + 15 = Rs. 21

Let the two numbers be x and y. Then,

x + y = 35   ……(i)

x – y = 13   …….(ii)

Adding equations (i) and (ii), we get

2x = 48

x = 48/2

x = 24

Putting x = 24 in (i), we get

x + y = 35

24 + y = 35

y = 35 – 24

y = 11

Hence, the two numbers are 24 and 11.

A system of simultaneous linear equations is said to be consistent, if it has at least one solution