This week we started to look at systems of liner equations, and something I learned is, how to determine how many solutions a line/system.
First I we must know what a solution and system are;
System: when 2 equations/lines cross, this a system
Solution: is the exact point where the lines/equations cross
To find out how many solutions there are you can simply look at the lines or equations, and seeing the patterns in an equation:
If an equation has 0/no solutions then they are parallel lines, where the slopes are the same but the intercepts aren’t, ex. 3x+#, 3x-# –> 3x=3x
And if an equation has 1 solution then the lines are perpendicular or oblique, where the slopes are different and one intercept is the same, ex. 3x – 4, -5x – 4 –> -4 = -4
So that leaves us with infinite solutions, this only occurs when the lines are equal to each other (the same line/ on top of each other), where every point is over lapping, ex. 3x+2 = 3x+2 (coincident lines)