x = 0 is the equation of
Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A.
Given :
1. Five years ago a was three times as old as b
2. Ten years later a shall be twice older than b.
Assume that present age of a as x and that of b as y.
Five years ago, a was thrice as old as b
i.e. age of a was x - 5 and age of b was 3(y-5)
x - 5 = 3 (y - 5)
x - 5 = 3y - 15
x - 3y = -15+5
x - 3y = -10 ---------(1)
Ten years later, a shall be twice as old as b
i.e. age of a will be x + 10 and age of b will be 2(y+10)
x + 10 = 2 (y + 10)
x + 10 = 2y + 20
x - 2y = 20-10
x - 2y = 10 ---------(2)
By elimination method, we get
x - 3y = -10
x - 2y = 10
- y = -20
y = 20 i.e. present age of b
Substituting y = 20 in equation 1, we get
x - 3y = -10
x - 3(20) = -10
x - 60 = -10
x = -10 + 60
x = 50 i.e. present age of a.
How many lines pass through two points?
Only one straight line can pass through two points because the line will connect the two points as one as the initial and another point as the ending point.
The graph of y = 4x will
For the equation 5x – 7y = 35, if y = 5, then the value of ‘x’ is
y = 0 is the equation of
Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines. Find the total number of customers.
Step-by-step explanation:
Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines.
Let say There are C customers in a Line and total L number of lines
Total number of customers = ( customers in a line) * (number of Lines)
=>Total number of customers = CL
If one customer is extra in a line, then there would be two less lines
=> Total number of customers = (C + 1)(L -2)
(C + 1)(L -2) = CL
=> CL + L - 2C - 2 = CL
=> L - 2C = 2 - eq 1
If one customer is less in line, there would be three more lines.
=> Total number of customers = (C - 1)(L +3)
(C - 1)(L +3) = CL
=> CL - L + 3C - 3 = CL
=> - L + 3C = 3 - eq 2
Adding eq 1 & eq 2
=> C = 5
L - 2(5) = 2
=> L = 12
5 customers in a Line
Total Number of customers = CL = 5*12 = 60
How many lines pass through one point?
For what value of ‘k’, x = 2 and y = -1 is a solution of x + 3y – k = 0?
The area of the triangle formed by the line 2x + 5y = 10 and the coordinate axes is
The graph of the linear equation x + y = 0 passes through the point
The graph of the linear equation x + y = 0 passes through the point (1,-1) because the co-ordinate of x and y axis satisfy the given equation
x + y = 0
1 - 1 = 0
so we can say (1,-1) is a solution of above equation
The graph of the linear equation x + y = 0 passes through the point
The equation of a line parallel to x-axis and 3 units above the origin is
Which of the following pair is a solution of the equation 3x – 2y = 7?
Express ‘y’ in terms of ‘x’ in the equation 5x – 2y = 7.
A fraction becomes 1/3 when 1 is subtracted from its numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction
If (k, -3) lies on the line 3x – y = 6, then the value of ‘k’ is
Putting x= k and y= -3 in the given equation,
i.e. 3(k) - (-3) = 6
=> 3k + 3 = 6
=> 3k = 3
Hence, k = 1
The equation of a line parallel to x-axis and 5 units below the origin is
Which of the following is a linear equation in two variables?
Express ‘x’ in terms of ‘y’ in the equation 2x – 3y – 5 = 0.
The point of the form (a, a), where a ¹ 0 lies on
If x = 3 and y = -2 satisfies 2x – 3y = k, then the value of ‘k’ is
The equation of a line parallel to the y-axis and 4 units above the origin is
x = 5 and y = -2 is the solution of the linear equation
x – 4 is the equation of
we know that the line parallel to y axis is given by x = a
x-4 = 0
x = 4
so it is a line parallel to y axis, at a distance of 4 units from it, to the right.
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