what are the solutions of the two equations x+2y=4 and 3x+6y = 12? how many solutions are possible? what are the realtions between cofficients of x . cofficients of y and constant terms in both the equations? what conclusion can you drawn when two equations are given but the graph is only one line?
Answers
The lines x+2y=4 -----(1) and 3x+6y = 12 ------(2) are the same lines , as the line (2) is three times the product of the line (1).
The number of possible solutions are infinite as both the lines are the same.
The ratio of coefficient of x , y and the constant term of the equation (1) upon (2) is equal to 1/3.
When two equations are given but the graph is only one line then it means the equations are coincident.
There are no solutions of the two equations x+2y=4 and 3x+6y = 12.
The given equations are x+2y=4 and 3x+6y = 1
The realtions between cofficients of x, cofficients of y and constant terms in both the equations are given by,
a1 = 1, a2 = 3, b1 = 2, b2 = 6, c1 = 4 and c2 = 12
a1/a2 = 1/3
b1/b2 = 2/6 = 1/3
c1/c2 = 4/12 = 1/3
Therefore, we have,
a1/a2 = b1/b2 = c1/c2 = 1/3
Therefore, the given equations represent the parallel lines.
As they do not intersect, so there are no solutions.