SOLUTION: Solve the following system of equations by ELIMINATION. State the solution. 10x+5y=10 6x+3y=6 So far this is what I have: -3(10x+5y=10) 5( 6x+3y= 6)

Question 417958: Solve the following system of equations by ELIMINATION. State the solution.
10x+5y=10
6x+3y=6

So far this is what I have:
-3(10x+5y=10)
5( 6x+3y= 6)
=
-30x-15y=-30
30x+15y=30
And they all cancel out,
so what do I put as my answer?

Answer by algebrahouse.com(1659) (Show Source): You can put this solution on YOUR website!
-30x - 15y = -30
30x + 15y = 30
---------------
0 = 0
= infinite solutions

When the variable disappears and you get a true statement, such as 0 = 0,
then there are "infinite solutions". This means, the two lines intersect
in an infinite number of points. In other words, the two equations are equivalent,
and would create the same line when graphed.

When the variable disappears and you get a false statement, such as 0 = 3,
then thee is "no solution". This means, the two lines would not intersect.
In other words, the two equations, when graphed, would create parallel lines.
www.algebrahouse.com

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