Leon A.

asked • 07/07/16

How many solutions are there for the following equation?

Y=x-3 and 2y+3=2x-3

1 Expert Answer

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Jess G. answered • 07/07/16

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let's solve using substitution
 
we know from the original equation: y = x-3 and 2y+3=2x-3
if we substitute for y, we get the equation: 2(x-3)+3=2x-3
let's simplify:
2x-6+3=2x-3
2x-3=2x-3
2x=2x
x=x
this identity is true for all real numbers one could substitute for x
therefore, there is an infinite number of solutions
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Kenneth S.

There are not two distinct equations, i.e. the second one can be simplified to y = x-3 also. Therefore it's only one line. That's infinitely many points. this situation is called DEPENDENT. Any two lines either meet at one point, or no points (if they have same slope but differing  y-intercepts), or in the case of dependent equations, infinitely many points.
 
You can always analyze this by putting each equation into y = mx + b form and comparing the two results.
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07/07/16

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