Linear Equations in Two Variables Test

Result

Linear Equations in Two Variables Test - 2

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which of the following equations has (3, -4) as its solution?

A
11x + 15y = -27

B
3x + 6y = 23

C
-14x + 13y = -33

D
18x – 4y = -35

Solution

The solution (3, -4) can satisfy the equation 11x + 15y = -27.

11 × 3 + 15 × (-4) = -27
33 – 60 = -27
-27 = -27

So, the equation 11x + 15y = -27 has (3, -4) as its solution.
Question 2
1 / -0

In a basketball match, Team A and Team B scored the number of the three pointers equal to Team C, which scored 20 three pointers. It was found that the score was miscalculated and was therefore calculated again. It was found that Team C scored 30 three pointers and Team B scored 13 three pointers. It was found that coincidentally the number of three pointers scored by Team A was same as the previous result.

What was the number of three pointers scored by Team D, if the numbers of three pointers of Team B (actual), Team A (actual) and Team B (miscalculated) when add up make the same score as Team D?

A
37

B
3

C
33

D
30

Solution

Given,
Team C scored 20 three pointers when the result was miscalculated.
Let the number of three pointers scored by Team A when the core was miscalculated be a.

And the number of three pointers scored by Team B when the score was miscalculated be b.
Therefore,
a + b = 20 ... (1)

Now, when the score was calculated again:
Team B scored 13 three pointers and Team C scored 30 three pointers.
Therefore,

Team A scored 30 – 13 = 17.
Therefore, Team A scored 17 three pointers in actual and it is the same number of three pointers when the result was miscalculated.
Now, equation (1) becomes:

17 + b = 20
b = 20 – 17
b = 3

Miscalculated result for Team B = 3 three pointers
Now,

The numbers of three pointers of Team B (actual), Team A (actual) and Team B (miscalculated) when add up makes the same score as Team D.
Number of three pointers scored by Team D = 17 + 13 + 3 = 33
Hence, 33 is the answer.
Question 3
1 / -0

Ram is paid Rs. 50 for delivering letters at the end of the week. On delivering each letter, he is paid Rs. 2. Shyam is paid Rs. 20 for delivering birthday cards at the end of each week. On delivering each card, he is paid Rs. 5. The money that Ram gets after a week is exactly the same as the money Shyam gets after two weeks.
(Assume that the number of letters delivered by Ram is x and the number of birthday cards delivered by Shyam is y.)

Which of the given options satisfies the above situation?

A
10y - x = 5

B
5y - x = 5

C
10y - x = 10

D
5y - 2x = 10

Solution

Given: The number of letters delivered by Ram is 'x' and the number of birthday cards delivered by Shyam is 'y'.

Ram is paid Rs. 50 for delivering the letters at the end of the week. On delivering each letter he is paid Rs. 2.
Therefore, 50 + 2x is the total amount of money that Ram gets after a week.

Shyam is paid Rs. 20 for delivering birthday cards at the end of each week. On delivering each card he is paid Rs. 5.
Therefore, 20 + 5y is the total amount of money that Shyam gets after a week.

Therefore, 2(20 + 5y) will be the money that Shyam gets after two weeks.
It is given that Shyam gets the same amount of money in two week as Ram gets in one week.

Therefore,
50 + 2x = 2(20 + 5y)

50 + 2x = 40 + 10y
50 - 40 = 10y - 2x

10 = 10y - 2x
2(5y - x) = 10
5y - x = 5