Mathematics Assignment Sheet

Section:7.1
Solution.1:
Given:
y+ 3x = 5.................(1)
2x + y = 10..............(2)
Ordered pair = (1,8)
So, x = 1, y =8;
By putting the value of x and y in equation 1;
8 + 3(1) = 5
11 = 5
L.H.S is not equal to R.HS.
Hence the ordered pair is not the solution of equation (1)
Now, By putting the value of x and y in equation 2;
2(1) + 8 = 10
10 = 10
L.H.S is equal to R.HS.
Hence the ordered pair is the solution of equation (2)
Solution.2:
Given:
3x- y =4...........(1)
2x + 2y = 12......(2)
From equation (2);
2x = 12 - 2y
x = 6 – y........(3)
By substituting the value of x in equation (1);
3(6 – y) - y =4

18 – 3y – y = 4
-4y = 4-18
y = 14/4
By substituting the value of y in equation (3);
x = 6 – 14/4
x = (24-14)/4
x= 10/4.
Solution.3:
Given:
7x + y = 15.............(1)
-2x + 3y = -1............(2)
Multiplying equation (1) with 3;
21x +3y = 15..............(3)
-2x +3y = -1
+ - +
---------------------
19x = 16
x = 16/19
Substituting the value of x in equation (1);
7 × 16
19 + y = 15
y = 173 /19
Solution.4:
Given:
x + 2y = -4.............(1)

-2x + 3y = -13............(2)
Multiplying equation (1) with 2;
2x +4y = -8..............(3)
-2x +3y = -13
+ - +
---------------------
y = 5
Substituting the value of y in equation (1);
x + 2(5) = -4
x = -14
Graphical:
Solution.5:
Given:
5x +3y = 12..............(1)
-10x – 6y = 8............(2)
In equation(1)
If, x =0;
Then y = 12/3 = 4; (0,4)
If, y =0;
Then x = 12/5 = 2.4; (2.4,0)
In equation(2)
If, x =0;
Then y = -8/6 = 1.33; (0,1.33)
If, y =0;
Then x = -8/10 = 0.8; (0.8,0)

Because, these points slope are intersecting each other so it is a consistent system and having
one solution.
Real-World Applications:
Solution.6:
Given:
C(x) = 55x + 15000
x = Total number of attendees
Venue charges = $70/ticket.
Revenue, r(x) = 70x
C(x) = r(x)
55x + 15000 = 70x
15000 = 70x - 55x
15000 = 15x
Sold tickets, x = 1000;
Venue breakeven for 1000 tickets;
C(1000) = 55 × 1000 + 15000
C(1000) = 70,000

Solution.7:
Given:
cost = 15,000
each floral arrangement costs = 17$
each arrangement sold costs = 25$
Profit from each arrangement = 25 - 17 = 8$
Number of Arrangements for Break-Even = 15,000/8 = 1875$
Solution.8:
Parameters Total amount of
solution
Percentage Saline Total amount of
Saline
Starting solution 20 35% 7
Solution Added x 15% 0.15x
Resulting Solution 20+x 48% 0.48(20+x) = 0.15x
+7
0.48(20+x) = 0.15x +7
9.6 + 0.48x = 0.15x +7
x = -7.87
15% of solution mixture = -7.87 × 0.15 = -1.181Gallons
For 48% of solution mixture:
20 + (-0.787) = 12.13
12.13 × 0.48 = 5.8244 Gallons
Solution.9:
Suppose,
Price of children admission = x
Price of Adults admission = y
So,
4x + 2y = 133.50 $ ....................(1)

6x +4y = 235.50$ .....................(2)
Multiplying with 2 in equation (1);
8x + 4y = 267.00$ ................(3)
6x +4y = 235.50$ .....................(2)
- - -
-----------------------------------------------
2x = 31.50
x = 15.75 $
Substituting the value of x in equation (1);
4 × 15.75 +2y = 133.50
63 +2y =133.50
2y = 70.5
y = 35.25$