SOLUTION: elimination 2a-4b=6 -a+2b=-3

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Question 1066585: elimination 2a-4b=6
-a+2b=-3

Found 3 solutions by stanbon, MathTherapy, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
elimination
2a-4b=6
-a+2b=-3
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Modify::
-a + 2b = -3
-a+2b = -3
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Ans: True for all (a,(a-3)/2) where a is any value.
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Cheers,
Stan H.
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Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

elimination 2a-4b=6
-a+2b=-3

2a - 4b = 6 -------- eq (i)
- a + 2b = - 3 ------ eq (ii)
a - 2b = 3 -------- Factoring out GCF, 2 in eq (i) ------ eq (iii)
0 = 0 -------- Adding eqs (iii) & (ii)
The system has: INFINITELY many solutions

Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website!
.
Your equations are EQUIVALENT, so actually it is ONE equation, not two.

Therefore, the "system" has INFINITELY many solutions.

These two equations represent ONE STRAIGHT line in a coordinate plane, and all points on this line are the "solutions".

For more details see the lesson
    - Geometric interpretation of a linear system of two equations in two unknowns
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Systems of two linear equations in two unknowns".