Solve the system of equations. y = 4x+1
y= x + 2x - 2
A. (-3, 13) and (1, -3)
B. (-1,-3) and (3, 13)
c. (-1,3) and (-3, 13)
D. (-3,-13) and (1,3)

none of the answers is correct!

Step-by-step explanation:

y = 4x+1

y= x + 2x - 2 which is y = 3x - 2

4x+1 = x + 2x - 2

x = - 3

substitute in y = 4x+1

y = 4 * -3 + 1

y = -12 + 1

y = -11

So the only point both lines have in common is the intersection between them at the point ( -3, - 11 )

By this knowledge Alone, you can exclude THREE (!) answers a, c an d, because the point ( -3, ...) should have been point ( -3, - 11 ) and therefore the answers a, c an d are beyond any doubt WRONG.

If there is at least one right answer, then the only one answer left, is answer b.

By now it is absolutely clear that answer b must be the right answer and you are done!

EXTRA

Although you have deduced beyond any doubt, that answer b must be the right answer, you still can check your findings 'to be sure' by looking and substituting both points in answer b...

BE CAREFUL, ONLY DO THIS IF YOU HAVE ENOUGH TIME. Again, you already know the right answer, and this is "just to confirm", so what is the harm in that?

By double checking yourself, it will sort of "undermine" your appproach. Basically you are doing something which is strictly spoken not nessasary any more. So I urge you to basically step over the urge to check yourself, and stick to your answer.

If you check the points (-1,-3) and (3, 13) in y = 4x+1 and

y= x + 2x - 2 you get this

Substitute point (-1,-3) in y = 4x+1 :

-3 = 4*-1 + 1 so -3 = -4 +1 which gives the TRUE statement -3 = -3.

Substitute point (-1,-3) in y= x + 2x - 2 :

-3 = -1 + 2*-1 - 2 so -3 = -1 -2 -2 which gives the FALSE statement -3 = -5. this means the answer b is not correct afterall.

This is kind of upsetting because apparently none of the answers is correct!

y= x + 2x - 2 you get this

`1234567890-=/*-qwertyuiop[]asdfghjkl; '\\zxcvbnm,./+ /