Question

Solve the following questions with clear explanations...

Points: 25 ☺

Answer 1

8) let
( 3x + y) = P
( 3x -y) = Q

1/P + 1/Q = 3/4 ------(1)

1/2P - 1/2Q = -1/8

1/P - 1/Q = -1/4 --------------(2)

add equation (1) and (2)

2/P = 1/2

P = 4 put in equation (1) Q = 2

hence,

P = 3x + y = 4 ----------(3)
Q = 3x - y = 2 -------(4)

add eqns (1) and (2)
6x = 6
x = 1 and y = 1

==×====×===×==×=====×=×=====×==×=×=×

9) let x litres of solution in which 50% acid mixed with y litres of solution in which 25% acid contain.

acid contains in 1st case 50x/100 litrres = x/2 L

water contains = (100-50)x/100 = x/2 L

second case
============
acid contains = 25y/100 = y/4 L
water contains = (100-25)y/100 = 3y/4 L

now,
in mixture
===========
acid contains = 10× 40/100 = 4L
water contains = 10× 60/100 = 6L

so,
amount of acid in 1st + amount of acid in 2nd = amount of acid in mix

x/2 + y/4 = 4 --------(1)

similarly for water

x/2 + 3y/4 = 6 ----------(2)

solve both eqns
2y/4 = 2
y = 4
and x = 6

hence , 50% concentrate solution = 6 L
and 25℅ concentrate soln = 4 L

====×==========×======×===

11) x + 3y = 6------------(1)

3x + 9y = 12
3( x +3y ) = 12
x + 3y = 4 ----------(2)

equation (1) and (2) are parallel line ,
see the graph
where red line is x +3y = 4
this cut at the x -axis at x = 4

and blue line is x +3y = 6
this cut at the x-axis at x = 6
========××××××=======

Answer 2

Answer:

The above answer is correct because....