SOLUTION: The solution set for the system 6x+9y=15 and 4x+6y=10 is best described as: a) undefined b) x=1, y=1 c) {(x,y)|y=(-2/3)x + (5/3)} d) inconsistent e) set of all points

Question 249679: The solution set for the system 6x+9y=15 and 4x+6y=10 is best described as:
a) undefined
b) x=1, y=1
c) {(x,y)|y=(-2/3)x + (5/3)}
d) inconsistent
e) set of all points
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
What do you notice if you divide the first by 3 and the second by 2?
correct they are the same
if you solve those two equations for y you will see that
4x+6y=10
6y=10-4x
y=10/6-4x/6
y=-2x/3+5/3
6x+9y=15
9y=15-6x
y=15/9-6x/9
y=-2x/3+5/3
They are equivalent equations with the same points
So answer c is correct
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The solution set for the system 6x+9y=15 and 4x+6y=10 is best described as:
---------
Write each equation in slope-intercept form to see that both
have a slope of -2/3
So the lines are parallel and never meet.
------
Ans: d
because, if you assume x and y have the same meaning in the two
equations, you are assuming something which is not true. So the
system is said to be inconsistent.
--------
Cheers,
Stan H.
======================
a) undefined
b) x=1, y=1
c) {(x,y)|y=(-2/3)x + (5/3)}
d) inconsistent
e) set of all points

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