Write whether the following statements are True or False? Justify your answers.
(i) ax + by + c = 0, where a, b and c are real numbers, is a linear equation in two variables.
(ii) A linear equation 2x + 3y = 5 has a unique solution.
(iii) All the points (2, 0), (–3, 0), (4, 2) and (0, 5) lie on the x-axis.
(iv) The line parallel to the y-axis at a distance 4 units to the left of y-axis is given by the equation x = – 4.
(v) The graph of the equation y = mx + c passes through the origin
The point of the form (a, – a) always lies on the line
(A) x = a (B) y = – a (C) y = x (D) x + y = 0
The point of the form (a, a) always lies on :
(A) x-axis (B) y-axis
(C) On the line y = x (D) On the line x + y = 0
How many linear equations in x and y can be satisfied by x = 1 and y = 2?
(A) Only one (B) Two (C) Infinitely many (D) Three
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation :
(A) Changes
(B) Remains the same
(C) Changes in case of multiplication only
(D) Changes in case of division only
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point
(A) (0, 2) (B) (2, 0) (C) (3, 0) (D) (0, 3)
The positive solutions of the equation ax + by + c = 0 always lie in the
(A) 1st quadrant (B) 2nd quadrant
(C) 3rd quadrant (D) 4th quadrant
In what ways did the British change
their policies as a result of the
rebellion of 1857?
If a linear equation has solutions (–2, 2), (0, 0) and (2, – 2), then it is of the form
(A) y – x = 0 (B) x + y = 0
(C) –2x + y = 0 (D) –x + 2y = 0
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