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The cost of a chair is half of the cost of a dining table. The linear equation representation of the above will be:
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
The value of k, if, (3, 2) is a solution of equation 4x + y = k is:
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
If α^{2}x + ay = 3, is satisfied by x = 1, y = 2, then the value of α will be:
Here (1, 2) α^{2}x + αy  3 = 0
then α^{2} (1) + α(2)  3 = 0
⇒ α^{2} + 2α  3 = 0
⇒ α^{2} + 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
The equation x  y + 1 = 0 is satisfied by x = α^{2} and y = α, then α =
(α^{2}, a) is a solution of the equation
x  y + 1 = 0
⇒ α^{2}  a + 1 = 0
⇒ The above equation has negative discriminant.
∴ value of a cannot be determined
If the equation x + 3y + 4k = 6 is satisfied by (2, 3) then the value of k is:
(2, 3) satisfies the equation x + 3y + 4k = 6,
then,
2 + 3 (3) + 4k = 6
⇒ 2 + 9 + 4k = 6
⇒ 4k = 5
⇒ k = 5/4
If the equation k (x^{3}  y^{3}) = (x^{2} + y^{2} + xy) and y = 1k , then the value of x is
k (x^{3}  y^{3}) = x^{2} + y^{2} + xy
The equation, (x + y) + = 12, then, u = ??, if x = 8
⇒ The equatios will be reduced to
Let ,
Arun and Kajol together contributed 100 rupees for the Prime Minister Relief fund. If the money donated by Arun is Rs 80 less than twice the money donated by Kajol then the money donated by Arun is:
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
If the point (4, 5) lies on the graph 3y = ax + 3, then a =
Point (4, 5) lies on the graph of the equation 3y = αx + 3
∴ 3 × 5 = 4α + 3
⇒ 4α = 12
⇒ α = 3
If C = where C denotes the temperature in Celsius and F denotes the temperature in Fahrenheit, The temperature (in Celsius) at which the numerical value on the both scales is same will be
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.
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