Archives

Show that the points A (1, 2), B ( – 1, – 16) and C (0, – 7) lie on the graph of the linear equation y = 9x – 7.

Given The linear equation y = 9x – 7. To Prove The points A (1, 2), B ( – 1, – 16) and C (0, – 7) lie on the graph of the... View Article

Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

Solution According to the given details A linear equation such that each point on its graph has an ordinate(y) which is 3 times its... View Article

Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

Solution According to the given details The linear equation, x + y = 10 We get, x = 10 – y Values of x and y satisfying the... View Article

Draw the graph of the equation represented by a straight line which is parallel to the x-axis and at 3 units below.

Solution According to the given details The linear equation, y = – 3 Values of x and y satisfying the equation are tabulated below... View Article

Determine the point on the graph of the linear equation 2x + 5y = 19 whose ordinate is 11/2 times its abscissa.

Solution From the given details 2x + 5y = 19 …(i) It is mentioned that Ordinate is times its abscissa ⇒ y = x... View Article

Draw the graphs of linear equations y = x and y = – x on the same Cartesian plane. What do you observe?

Solution Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0,... View Article

The graph given below represents the linear equation x + y = 0. Write whether the following statement is True or False? Justify your answer.

The given statement is True. Solution Given equation x + y = 0. x = – y From the graph, we get the points ( – 3, 3) and (... View Article

The graph of the linear equation x + 2y = 7 passes through the point (0, 7). Write whether the following statement is True or False? Justify your answer.

The given statement is False. Solution Given equation x + 2y = 7. On ubstituting the values of x = 0 and y = 7 from the point (0, 7) in the... View Article

The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12. Write whether the following statement is True or False? Justify your answer.

The given statement is True. Solution Given equation 3x + 4y = 12. On ubstituting the values of x = 0 and y = 3 from the point (0, 3) in... View Article

The equation of x – axis is of the form A. x = 0 B. y = 0 C. x + y = 0 D. x = y

The correct answer is B. y = 0 Solution The points on the x-axis are of the form (a, 0), where a is any real number. The y-coordinate of the... View Article

Any point on the line y = x is of the form A. (a, a) B. (0, a) C. (a, 0) D. (a, – a)

The correct answer is A. (a, a) Solution Any point on the line y = x will have x and y coordinate the same. So, any point on the line y = x is... View Article

Any point on the x – axis is of the form A. (x, y) B. (0, y) C. (x, 0) D. (x, x)

The correct answer is C. (x, 0) Solution Any point on the x-axis has its ordinate 0. So, any point on the x-axis is of the form (x, 0).... View Article

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

The correct answer is B. 1. x + 0. y = 7 Solution The Coefficient of y in the given equation x =7 is 0. So, the equation can be expressed... View Article

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)

The correct answer is D. (0, 2)Solution Let 2x + 3y = 6 cut the y-axis at P. T Therefore at P x-coordinate = 0. On substituting x =... View Article

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)

The correct answer is A. (-9/2 , m) Solution Solving the above equation 2x + 0y + 9 = 0 we obtain, 2x = -9 x = -9/2 As the... View Article

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

The correct answer is A. 4Solution We know that, (2, 0) = (x, y) Substituting values of x and y in the given equation, we get... View Article

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

The correct answer is A. Natural numbersSolution Consider, 2x + 5y = 7 x 1 y 1 A. (1, 1) is a solution of 2x + 5y = 7... View Article

The linear equation 2x – 5y = 7 has A. A unique solution B. Two solutions C. Infinitely many solutions D. No solution

The correct answer is C. Infinitely many solutionsSolution By expressing y in terms of x in the equation 2x – 5y = 7, we obtain, 2x... View Article

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.

Solution Let us plot the graph as per the given details. Then the graph can be represented as follows From the graph, we observe that, The... View Article

Points A (5, 3), B (-2, 3) and D (5, -4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

Given Points A (5, 3), B (–2, 3) and D (5, –4) are three vertices of a square ABCD Find out We have to determine the coordinates... View Article

M	T	W	T	F	S	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30