Write whether the following statements are True or False? Justify your

1.	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.
Answer» (i) False, because ax + by + c = 0 is a linear equation in two variables if both a and b are non-zero. (ii) False, because a linear equation in two variables has infinitely many solutions. (iii) False, the points (2, 0), (–3, 0) lie on the x-axis. The point (4, 2) lies in the first quadrant. The point (0, 5) lies on the y-axis. (iv) True, since the line parallel to y-axis at a distance a units to the left of y-axis is given by the equation x = – a. (v) False, because x = 0, y = 0 does not satisfy the equation.

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.

Answer»

(i) False, because ax + by + c = 0 is a linear equation in two variables if both a and b are non-zero.

(ii) False, because a linear equation in two variables has infinitely many solutions.

(iii) False, the points (2, 0), (–3, 0) lie on the x-axis. The point (4, 2) lies in the first quadrant. The point (0, 5) lies on the y-axis.

(iv) True, since the line parallel to y-axis at a distance a units to the left of y-axis is given by the equation x = – a.

(v) False, because x = 0, y = 0 does not satisfy the equation.