SOLUTION: My question is find what x and y is. The equations are: x - y = 5 and x * y = 8

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Question 902317: My question is find what x and y is.
The equations are:
x - y = 5
and
x * y = 8
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

here you have system to solve; you can do it by substitution, by elimination, or by graphing
x+-+y+=+5............eq.1
x+%2A+y+=+8..........eq.2
________________________________________let's use substitution
start with x+-+y+=+5............eq.1 and solve it for y
x+-+5+=+y............substitute in eq.2
x+%2A+%28x-5%29+=+8 ..........solve it for x
x%5E2-5x+=+8
x%5E2-5x+-8=0....use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-+%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A+%28-8%29%29%29%2F%282%2A1%29+

x+=+%285+%2B-+sqrt%28+25%2B32%29%29%2F2+
x+=+%285+%2B-+sqrt%28+57%29%29%2F2+
x+=+%285+%2B-+7.6%29%2F2+
solutions:
x+=+%285+%2B+7.6%29%2F2+
x+=+12.6%2F2+
x+=+6.3+
or
x+=+%285+-+7.6%29%2F2+
x+=+-2.6%2F2+
x+=+-1.3+

now find y
x+-+y+=+5............eq.1...if x+=+6.3+

6.3+-+5+=+y

1.3+=+y

and
x+-+y+=+5............eq.1...if x+=+-1.3+

-1.3+-+5+=+y

-6.3+=+y

so, one pair of solutions is:
x+=+6.3+ and 1.3+=+y
the other is
x+=+-1.3+ and -6.3+=+y

check:

x+%2A+y+=+8 ..........eq.2..plug in x+=+6.3+ and 1.3+=+y

6.3+%2A+1.3+=+8
8.19+=+8 ...round to whole number
8=+8

x+%2A+y+=+8 ..........eq.2..plug in y+=+-6.3+ and -1.3+=+x

-1.3+%2A+%28-6.3%29+=+8
8.19+=+8 ...round to whole number
8=+8


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
My question is find what x and y is.
The equations are:
x - y = 5
and
x * y = 8
--------------------------------------------------------------

Solve the first equation for x

x+-+y+=+5

x+-+y%2By+=+5%2By

x+=+5%2By

Then plug that into x+%2A+y+=+8

x+%2A+y+=+8

%285%2By%29+%2A+y+=+8

y%2A%285%2By%29+=+8

y%2A5%2By%2Ay+=+8

5y%2By%5E2+=+8

5y%2By%5E2-8+=+0

y%5E2%2B5y-8+=+0

Now use the quadratic formula to solve for y

y+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

y+=+%28-%285%29%2B-sqrt%28%285%29%5E2-4%281%29%28-8%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+5, c+=+-8

y+=+%28-5%2B-sqrt%2825-%28-32%29%29%29%2F%282%29

y+=+%28-5%2B-sqrt%2825%2B32%29%29%2F%282%29

y+=+%28-5%2B-sqrt%2857%29%29%2F2

y+=+%28-5%2Bsqrt%2857%29%29%2F2 or y+=+%28-5-sqrt%2857%29%29%2F2

y+=+1.274917 or y+=+-6.274917 These are approximate

Finally, you would use these solutions to find x (plug them into x+=+5%2By). I'll let you do this part.