Which could be the total number of solutions to the system of equation? a. no solution b 1 solution c 2 solutions d 3 solutions e infinitely many solution
Oh, I see......he/she meant any system of two linear equations.....
We could have infinitely many solutions as the greatest number.......this occurs when one line lies atop another.......
linear equations are lines.
If the lines are the same there will be an infinite number of solutions.
ex
2x+4y=8 and 6x+12y=24 See how I just multiplied all the coefficients and the constant by 3.
or if the lines cross each other there will be just 1 solution
or if the lines are parallel they will never cross and there will be NO solutions!
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I am referring only to 2 dimensional linear equations ( x and y but no z)
Although the result is the same for three dimensional lines except that there may be no solutions becsause the lines are skew. They do not need to be parallel. ://