Asked by Kim

Solve by substitution or elimination method:

4x – 5y = 14
-12x + 15y = -42

when i try this solution i end up cancelling out the whole problem. can someone please help me!
Answered by Reiny
that's because you are really given only one equation
if you multiply the first equation by -3 you get your second equation so by subtracting them you get
0 = 0
if that happens, there will be an infinite number of solutions, namely any point that satisfies the first equation.
Answered by Kim
what about this one? I'm having a tough time with this one as well...

Solve by substitution or elimination method: -2x + 6y = 19
10x – 30y = -15


Answered by Kim
with the first one was i suppose to multiply it by -3? i multiplied the first equiation by 15 and the second by -5. does it matter?
Answered by Sam
SUBSTITUTION: Solve for a variable in one equation and then substitute that value for the variable in the other equation.

ELIMINATION: Manipulate an equation so that one variable will be eliminated when you add the equations together. As long as one variable cancels, it doesn't matter how you choose to manipulate the equation (as long as you do the same things to all terms in the equation).
Answered by Kim
so can you tell me if this is correct....

4x – 5y = 14
-12x + 15y = -42


15(4x – 5y = 14) = 60x – 75y = 210
5(-12x +15y = -42) = -60x + 75y = -210

60x – 75y = 210
+ -60x + 75y = -210
= 0

The equations are not independent therefore they have an infinite solution set.
Answered by Kim
would it be correct to say that the equations are not independent therefore they have an infinite solution set.
Answered by Sam
No. They are DEPENDENT (the lines are right on top of each other when you graph them) so they have an infinite solution set.

INDEPENDENT means that there's one point that's independent of the others (the point of intersection or the single solution to both equations).
Answered by Sam
Oh, you said NOT independent. I missed the double negative there - sorry.