Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) Intersecting lines
(ii) Parallel lines
(iii) Coincident lines
(i) Given the linear equation 2x + 3y – 8 = 0.
To find another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines, it should satisfy below condition;
(a1/a2) ≠ (b1/b2)
Thus, another equation could be 2x – 7y + 9 = 0, such that;
(a1/a2) = 2/2 = 1 and (b1/b2) = 3/-7
Clearly, you can see another equation satisfies the condition.
(ii) Given the linear equation 2x + 3y – 8 = 0.
To find another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines, it should satisfy below condition;
(a1/a2) = (b1/b2) ≠ (c1/c2)
Thus, another equation could be 6x + 9y + 9 = 0, such that;
(a1/a2) = 2/6 = 1/3
(b1/b2) = 3/9= 1/3
(c1/c2) = -8/9
Clearly, you can see another equation satisfies the condition.
(iii) Given the linear equation 2x + 3y – 8 = 0.
To find another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines, it should satisfy below condition;
(a1/a2) = (b1/b2) = (c1/c2)
Thus, another equation could be 4x + 6y – 16 = 0, such that;
(a1/a2) = 2/4 = 1/2, (b1/b2) = 3/6 = 1/2, (c1/c2) = -8/-16 = 1/2
Clearly, you can see another equation satisfies the condition.