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Which of the following are the solutions of the equation 2x + 3y = 13?
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.
If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are):
Given equations are
3x + 16y = 13 and x + y = p
These equations may have many set of solutions commons for different values of p.
If x = k^{2} and y = k are solutions of equation x  5y = 6 then k =?
(k, k) will satisfy x  5y + 6 = 0
⇒ k^{2}  5k + 6 = 0
⇒ k^{2}  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
The solution of equation x  y + 8 = 0 is x = k^{3} and y = 0, then k =?
(k^{3}, 0) satisfies the equation, x  y + 8 = 0
⇒ k^{3}  (0) + 8 = 0
⇒ k^{3} = 8
⇒ k = (–8)^{1/3} = 2
If the equation (x + 3y)  (3x + y) + (x  y) = (α  b), then which of the following is a solution of the above equation?
x + 3y  3x  y + x  y = α  b
⇒  x + y = α + b
⇒ y  x = α  6
∴ (x, y) is satisfied by (b, α)
The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 is
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.
The point of intersection of 3x + 4y = 15 and xaxis will be
∴ The ordinate of every point on xaxis = 0
∴ The line 3x + 4y = 15 and the xaxis will intersect where value y of the line becomes zero
∴ 3x = 15
⇒ x = 5
∴ The point of intersection is (5, 0)
The graph of the equation 15x + 36y = 108 will cut the y axis at:
At y  axis, ordinate ≠ 0 abscissa = 0
∴ x = 0
⇒ 36y = 108
⇒ y = 3
∴ point of intersection = (0, 3)
The distance between the graphs of the equations x = 3 and x = 3 is
The distance between the graphs = 3  (3)
= 3 + 3 = 6 units
The equation 3x + 2y = 8 has
The equation can be written as,
∴ For different values of x, different values of y will exist.
∴ The above equation has many solutions.
The equation of the parallel to xaxis and passing through the point (3, 4) will be:
Equation of line parallel to xaxis, will be of the form y = constant.
∴ Desired equation of line y = 4
The equation 3x = 9 is pitied on graph paper, then which point lies on the graph?
Given 3x = 9
⇒ x = 9/3 = 3
∴ Line is parallel to yaxis and passes through x = 3
∴ Point (3, 9) will lie on 3x = 9
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
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
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:
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
In a ΔABC, ∠C = 3, ∠B = 2(∠A + ∠B), then ∠C =?
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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