Question

Form the pair of linear equations in the

following problems, and find their solutions

graphically.

1) 5 books and 7 pens together cost Rs.79 whereas

7 books and 5 pens together cost Rs.77. Find the

cost of 1 book and 2 pens. ​

Answer 1

Answer:

x=6 and y=7

Step-by-step explanation:

LET THE COST OF 1 BOOK BE x

AND THE COST OF 1 PEN BE y.

A.T.Q,

5x + 7y = 79 ----------(1)

7x + 5y = 77 ----------(2)

Let's solve your system by elimination.

5x+7y=79;7x+5y=77

Multiply the first equation by 5,and multiply the second equation by -7.

5(5x+7y=79)

−7(7x+5y=77)

Becomes:

25x+35y=395

−49x−35y=−539

Add these equations to eliminate y:

−24x=−144

Then solve−24x=−144for x:

−24x=−144

−24x

−24

=

−144

−24

(Divide both sides by -24)

x=6

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

5x+7y=79

Substitute6forxin5x+7y=79:

(5)(6)+7y=79

7y+30=79(Simplify both sides of the equation)

7y+30+−30=79+−30(Add -30 to both sides)

7y=49

7y

7

=

49

7

(Divide both sides by 7)

y=7

Answer:

x=6 and y=7

Answer 2

Step-by-step explanation:

b- book

p- pen

5b+7p=79 -----(1)

7b+5p=77------(2)

add equation (1) and (2).

12b+12p= 156

i.e. b+p=13

b=13-p-----(3)

subtract (2) from (1)

-2b+2p=2

-b+p=1-----(4)

put eq.(3) in (4)

-(13-p)+p=1

-13+p+p=1

2p=14

p=7------(5)

put eq (5) in (3)

b=13-7

b=6-----(6)

Therefore cost of 1 book and 2 pens is,

b+2p= 6+(2*7) = 6+14 =20

It will cost Rs. 20.