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Practice each question, then open the answer or worked solution.
The linear equation 2x – 5y = 7 has
A. A unique solution
B. Two solutions
C. Infinitely many solutions
D. No solution
C. Infinitely many solutions
Explanation:
Expressing y in terms of x in the equation 2x – 5y = 7, we get,
2x – 5y = 7
– 5y = 7 – 2x
y = ( 7 – 2x)/– 5
Hence, we can conclude that the value of y will be different for different values of x.
Hence, option C is the correct answer.
The equation 2x + 5y = 7 has a unique solution, if x, y are:
A. Natural numbers
B. Positive real numbers
C. Real numbers
D. Rational numbers
A. Natural numbers
Explanation:
Consider, 2x + 5y = 7
| x | 1 |
| y | 1 |
A. (1, 1) is a solution of 2x + 5y = 7
B. If positive real numbers are chosen, 2x + 5y = 7 will have many solutions.
C. If real numbers are chosen, 2x + 5y = 7 will have infinite solutions.
D. If rational numbers are chosen, 2x + 5y = 7 will have many solutions.
Hence, option A is the correct answer.
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is
A. 4
B. 6
C. 5
D. 2
A. 4
Explanation:
We know that,
(2, 0) = (x, y)
Substituting values of x and y in the above equation, we get
2×2 + 3×0 = k
k = 4
Hence, option A is the correct answer.
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form
A. (-9/2 , m)
B. (n, -9/2)
C. (0, -9/2)
D. ( – 9, 0)
A. (-9/2 , m)
Explanation:
Solving the above equation we get,
2x = -9
x = -9/2
As the coefficient of y is 0, therefore, y can take any value and will not affect our answer.
A. x = -9/2
y = any value
B. x = n
C. x = 0
D. x = -9
Hence, option A is the correct answer.
The graph of the linear equation 2x + 3y = 6 cuts the y – axis at the point
A. (2, 0)
B. (0, 3)
C. (3, 0)
D. (0, 2)
D. (0, 2)
Let 2x + 3y = 6 cut the y-axis at P. therefore at P x-coordinate = 0.
Substituting x = 0, we get
2(0) + 3y = 6
3y = 6
y = 2
Hence the coordinates are (0, 2).
A. (2, 0) is wrong because it has x = 2
B. (0, 3) is wrong because it has y = 3
C. (3, 0) is wrong because it has x = 3
D. (0, 2) is right because it has x = 0 and y = 2 which is equal to the coordinates (0,2)
Hence, option D is the correct answer.
The equation x = 7, in two variables, can be written as
A. 1. x + 1. y = 7
B. 1. x + 0. y = 7
C. 0. x + 1. y = 7
D. 0. x + 0. y = 7
B. 1. x + 0. y = 7
A. Simplifying the equation we get x + y = 7
B. Simplifying the equation we get x + 0y = 7 which is equal to x = 7
C. Simplifying the equation we get y = 7
D. simplifying the equation we get 0x + 0y = 7 which is not possible.
Hence, option (B) is the correct answer.
Any point on the x-axis is of the form
A. (x, y)
B. (0, y)
C. (x, 0)
D. (x, x)
C. (x, 0)
Any point on the x-axis has its ordinate 0.
So, any point on the x-axis if of the form (x, 0).
Hence, option (C) is the correct answer.
Any point on the line y = x is of the form
A. (a, a)
B. (0, a)
C. (a, 0)
D. (a, – a)
A. (a, a)
Any point on the line y = x will have x and y coordinate same.
So, any point on the line y = x is of the form (a, a).
Hence, option (A) is the correct answer.
The equation of x – axis is of the form
A. x = 0
B. y = 0
C. x + y = 0
D. x = y
B. y = 0
The equation of x-axis is y = 0, since, x-axis is a parallel to itself at a distance 0 from it.
Hence, option (B) is the correct answer.