SOLUTION: Find common solution algebraically for y=x^2+4x and 2y-y=1 Answer for this was (-1, -3)How do you get this? Please help and thank you.

Algebra ->  Trigonometry-basics -> SOLUTION: Find common solution algebraically for y=x^2+4x and 2y-y=1 Answer for this was (-1, -3)How do you get this? Please help and thank you.       Log On


   

Question 684378: Find common solution algebraically for y=x^2+4x and 2y-y=1 Answer for this was (-1, -3)How do you get this? Please help and thank you.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if (-1,+-3)
-3=%28-1%29%5E2%2B4%28-1%29
-3=1-4
-3=-3
2y-y=1
2%28-3%29-%28-3%29=1
-6%2B3=1
-3%3C%3E1

so, (-1,+-3) is not common solution

than common solution will be:
for y=x%5E2%2B4x and
2y-y=1...=>...y=1...plug it in y=x%5E2%2B4x and solve for x

1=x%5E2%2B4x
0=x%5E2%2B4x-1
or
x%5E2%2B4x-1=0....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+

x+=+%28-4+%2B-+sqrt%28+16%2B4+%29%29%2F2+

x+=+%28-4+%2B-+sqrt%28+20+%29%29%2F2+

x+=+%28-4+%2B-+4.47%29%2F2+

solutions:
x+=+%28-4+%2B4.47%29%2F2+
x+=+%280.47%29%2F2+
x+=+0.235
or
x+=+%28-4+-4.47%29%2F2+
x+=+-8.47%2F2+
x+=+-4.235



common solution (0.235,1) and (-4.235,1)