SOLUTION: write each equation in slope-intercept form. Then determine, without solving the system, whether the system has exactly one solution, no solution, or an infinite number of solution

Question 590619: write each equation in slope-intercept form. Then determine, without solving the system, whether the system has exactly one solution, no solution, or an infinite number of solutions 4x-3y=2 5x+3y=6
12x-9y=6 10x+6y=2
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
4x-3y=2
5x+3y=6
12x-9y=6
10x+6y=2

y = (4/3)x - 2/3
y = (-5/3)x + 2
y = (4/3)x - 2/3
y = -5/3)x + 1/3

2 of the lines have the same slope and the same y intercept so they are identical. if you graph these equations, they will look like one line rather than 2.
2 of the lines have the same slope and different y intercept so they are parallel.
you have 1 set of identical lines and 1 set of parallel lines that will intersect in 2 separate points on a graph.
for there to be a common solution, all 4 lines would have had to intersect in one common point on the graph.
since there is not one common solution for all 4 equations, this system of equations has no solution.

a graph of the lines will show the 2 points of intersection.

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