How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x-9y=6# and #2x-6y=-6#?

1 Answer
Feb 15, 2017

“Consistent” in linear equations means that they have at least one common solution. Graphically, that means that the two lines have an intersection point.


Using graph paper or a suitable software program, plot out the two equations. If they have an intersection point, they are “consistent”. If not, they are “inconsistent”. Graphing is a very useful visual technique in many cases. Finding common solutions to sets of equations it not really one of them, but it demonstrates the fact of later numerical solutions.

Numerically the equations can be rewritten in “standard form” to show that they have identical slopes (1/3). That means that they are parallel lines that never intersect, so the system is inconsistent. Graphically this is shown on the plot.
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