Without solving, determine the number of solutions for this system. What does the graph of the system look like?
2 answers:
Rewriting each equation in slope-intercept form, you have
... y = (3/2)x -5/4
... y = (3/2)x - 5/6
These lines have the same slope, but different intercepts. The appropriate description is ...
... A) no solution; parallel lines
Answer:Correct
no solution; parallel lines
You can determine the number of solutions for the system without solving by rewriting the equations in standard form and simplifying.
Rewrite the equations in standard form:
6x - 4y = 5
9x - 6y = 5
Factor out the GCF for each equation:
2(3x - 2y) = 5
3(3x - 2y) = 5
Simplify:
3x - 2y =
5
2
3x - 2y =
5
3
3x -2y cannot equal both
5
2
and
5
3
. Therefore the system doesn't have any solutions.
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Best of Luck!