Math Olympiad Test: Linear Educations in Two Variables- 1 - Class 9 MCQ

Let the cost of a chair be Rs. y and cost of dining table be Rs. x
According to the question
y = x/2
⇒ x = 2y

Given 4x + y = k
∴ (3, 2) is a solution of above equation
∴ (3, 2) will satisfy the above equation
∴  4 x 3 + 2 = 12 + 2 = 14 = k

Here (1, 2) α²x + αy - 3 = 0
then α² (1) + α(2) - 3 = 0
⇒ α² + 2α - 3 = 0
⇒ α² + 3α - α - 3 = 0
⇒ α(α + 3) - 1(α + 3) = 0
⇒ (α + 3) (α - 1) = 0
⇒ α + 3 = 0, or α - 1 = 0
α = -3, or α = 1

(α², a) is a solution of the equation
x - y + 1 = 0
⇒ α² - a + 1 = 0
⇒ The above equation has negative  discriminant.
∴ value of a cannot be determined 

(2, 3) satisfies the equation x + 3y + 4k = 6,
then,
2 + 3 (3) + 4k = 6
⇒ 2 + 9 + 4k = 6
⇒ 4k = -5
⇒ k = -5/4

k (x³ - y³) = x² + y² + xy

⇒ The equatios will be reduced to


Let ,

Let the amount donated by Kajol be rs x
∴ Amount donated by Arun = Rs. (2x - 80)
According to the question
x + 2x - 80 = 100
⇒ 3x = 180
⇒ x = 60
∴ Money donated by Arun = Rs (2 × 60 - 80) = Rs. 40

Point (4, 5) lies on the graph of the equation 3y = αx + 3
∴  3 × 5 = 4α + 3
⇒ 4α = 12
⇒ α = 3

Let the numerical value of temperature be x
∴ 
⇒ 9x = 5x -160
⇒ 4x = -160
⇒ x = -40
∴ the temperature is equal in both the scales at -40°C.