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Math Olympiad Test: Linear Educations in Two Variables- 2


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15 Questions MCQ Test Mathematics Olympiad for Class 9 | Math Olympiad Test: Linear Educations in Two Variables- 2

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Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 1

Which of the following are the solutions of the equation 2x + 3y = 13?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 1

The given linear equation is 2x + 3y = 13
Now substituting the values of x and y from option in equation (i), we see
For (a) 2 × 4 + 3 × 2 = 8 + 6 = 14 ≠ 13
∴ (a) is not correct option.
Again 2 × 2 + 3 × 3 = 4 + 9 = 13 = 13
∴ (b) is required answer.

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 2

If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are):

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 2

Given equations are
3x + 16y = 13 and x + y = p
These equations may have many set of solutions commons for different values of p.

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 3

If x = k2 and y = k are solutions of equation x - 5y = -6 then k =?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 3

(k, k) will satisfy x - 5y + 6 = 0
⇒ k2 - 5k + 6 = 0
⇒ k2 - 3k - 2k + 6 = 0
⇒ k(k -3) - 2(k - 3) = 0
⇒ (k -3) (k - 2) = 0
⇒ k - 2 = 0 or, k - 3 = 0
⇒ k = 2 or 3

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 4

The solution of equation x - y + 8 = 0 is x = k3 and y = 0, then k =?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 4

(k3, 0) satisfies the equation, x - y + 8 = 0
⇒ k3 - (0) + 8 = 0
⇒ k3 = -8
⇒ k = (–8)1/3 = -2

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 5

If the equation (x + 3y) - (3x + y) + (x - y) = (α - b), then which of the following is a solution of the above equation?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 5

x + 3y - 3x - y + x - y = α - b
⇒ - x + y = α + b
⇒ y - x = α - 6
∴ (x, y) is satisfied by (b, α)

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 6

The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 is

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 6

Let the point of intersection of lines be (a, b)
∴ 3α + 4b = 12 and 6α + 8b = 48
The above two equations have no solutions for (α, b)
∴ The graph will not intersect.

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 7

The point of intersection of 3x + 4y = 15 and x-axis will be

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 7

∴ The ordinate of every point on x-axis = 0
∴ The line 3x + 4y = 15 and the x-axis will intersect where value y of the line becomes zero
∴ 3x = 15
⇒ x = 5
∴ The point of intersection is (5, 0)

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 8

The graph of the equation 15x + 36y = 108 will cut the y- axis at:

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 8

At y - axis, ordinate ≠ 0 abscissa = 0
∴ x = 0
⇒ 36y = 108
⇒ y = 3
∴ point of intersection = (0, 3)

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 9

The distance between the graphs of the equations x = 3 and x = -3 is

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 9

The distance between the graphs = 3 - (-3)
= 3 + 3 = 6 units 

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 10

The equation 3x + 2y = 8 has

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 10

The equation can be written as,

∴ For different values of x, different values of y will exist.
∴ The above equation has many solutions.

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 11

The equation of the parallel to x-axis and passing through the point (3, -4) will be:

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 11

Equation of line parallel to x-axis, will be of the form y = constant.
∴ Desired equation of line y = -4

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 12

The equation 3x = 9 is pitied on graph paper, then which point lies on the graph?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 12

Given 3x = 9 
⇒ x = 9/3 = 3
∴ Line is parallel to y-axis and passes through x = 3
∴ Point (3, 9) will lie on 3x = 9 

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 13

The monthly incomes of A and B are in the ratio 8 : 7 and their expedites are in the ratio 19 : 16 If the savings of both A and B is Rs. 2500, then the month income of A is

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 13

Income of A = 8x, Income of B = 7x
Expenditure of A = 19y
Expenditure of B = 16y
According to the question
8x -19y = 2500
⇒ 7x -16 y 2500
⇒ From these two equations,
We have,
x = 1500, y = 500
∴ Income of A = Rs 8 × 1500
= Rs 12000

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 14

A man’s age is 3 times the sum of the ages of his 2 sons after 5 years, His age will be twice the sum of ages of his 2 sons. The age of man (in years) will be:  

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 14

Let the sum of ages of two sons be x, and their father’s age = y years
According to the question,
y = 3x
and y + 5 = 2(x + 10)
∴ 3x + 5 = 2x + 20
⇒ x = 15 years
and y = 45 years

Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 15

In a ΔABC, ∠C = 3, ∠B = 2(∠A + ∠B), then ∠C =?

Detailed Solution for Math Olympiad Test: Linear Educations in Two Variables- 2 - Question 15

We have ∠A + ∠B + ∠C = 180°
According to the question
∠C = 3, ∠B = 2 (180° - ∠C)
⇒ ∠C = 360 - 2∠C
⇒ 3∠C =  360°
⇒ ∠C = 120°

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