SOLUTION: y = {{{ sqrt x }}} + 4 y = 2x+1

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Question 188798: y = +sqrt+x+ + 4
y = 2x+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y+=++sqrt+%28x%29+%2B+4 Start with the first equation.


+2x+%2B+1+=++sqrt+%28x%29+%2B+4 Plug in y=2x%2B1


+2x+%2B+1+-4=++sqrt+%28x%29+ Subtract 4 from both sides.


+2x+-+3=++sqrt+%28x%29+ Combine like terms.


+%282x+-+3%29%5E2=++x+ Square both sides


+4x%5E2-12x%2B9=++x+ FOIL


+4x%5E2-12x%2B9-x=+0+ Subtract x from both sides.


+4x%5E2-13x%2B9=+0+ Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-13, and c=9


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-13, and c=9


x+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 Negate -13 to get 13.


x+=+%2813+%2B-+sqrt%28+169-4%284%29%289%29+%29%29%2F%282%284%29%29 Square -13 to get 169.


x+=+%2813+%2B-+sqrt%28+169-144+%29%29%2F%282%284%29%29 Multiply 4%284%29%289%29 to get 144


x+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%284%29%29 Subtract 144 from 169 to get 25


x+=+%2813+%2B-+sqrt%28+25+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%2813+%2B-+5%29%2F%288%29 Take the square root of 25 to get 5.


x+=+%2813+%2B+5%29%2F%288%29 or x+=+%2813+-+5%29%2F%288%29 Break up the expression.


x+=+%2818%29%2F%288%29 or x+=++%288%29%2F%288%29 Combine like terms.


x+=+9%2F4 or x+=+1 Simplify.


So the possible answers for "x" are x+=+9%2F4 or x+=+1


However, if you plug in x+=+1 into the equation +2x+%2B+1+=++sqrt+%28x%29+%2B+4, you'll find a contradiction. So this is an extraneous solution (ie we must ignore this value).


So the only solution for "x" is x+=+9%2F4


Now plug in x+=+9%2F4 into y=2x%2B1 to find "y"