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Question 547224: How many solutions are there for this equation?
2y = 2x + 24
-x + y = 12
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This system of equations would plot as two straight lines. For there to be a common solution, the lines need to intersect (i.e., one common solution) or lay one on top of another (i.e., an infinite set of common solutions).
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The easiest way to determine this is to simplify the equations and rewrite them so they are in the same form for inspection or solution. The general form for these type of linear equations is: y = mx + b, where m, the coefficient of x, is the slope of the line and b is the y intercept (where x = 0).
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2y = 2x + 24 is close to the standard form; however, we see all terms in the equation have 2 as a factor and thus 2 can be factored out (divide both sides by 2):
y = x + 12
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-x + y = 12 looks suspiciously like the first equation. Let's simplify by adding x to both sides so that y is by itself on the left side of the equation:
y = x + 12
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Ah, ha! 8-) The equations are the same. There is an infinite number of solutions between the two equations.
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Cheers,
Lee
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