SOLUTION: Find the real solutions, if any, of each system. {4x^2 + 9y^2= 36} {y= x+3} I get stuck after setting everything to zero! Thankyou

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the real solutions, if any, of each system. {4x^2 + 9y^2= 36} {y= x+3} I get stuck after setting everything to zero! Thankyou      Log On


   

Question 30000: Find the real solutions, if any, of each system.
{4x^2 + 9y^2= 36}
{y= x+3}
I get stuck after setting everything to zero!
Thankyou
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
[1] 4%2Ax%5E2+%2B+9%2Ay%5E2=+36
[2] y+=+x%2B3
Substitute y+=+x%2B3 in [1]
4%2Ax%5E2+%2B+9%2A%28x+%2B+3%29%5E2+=+36
4%2Ax%5E2+%2B+9%2A%28x%5E2+%2B+6%2Ax+%2B+9%29+=+36
4%2Ax%5E2+%2B+9%2Ax%5E2+%2B+54%2Ax+%2B+81+=+36
13%2Ax%5E2+%2B+54%2Ax+%2B+45+=+0
use
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-54+%2B-+sqrt%28+54%5E2-4%2A13%2A45+%29%29%2F%282%2A13%29+
x+=+%28-54+%2B-+sqrt%28+2916-2340+%29%29%2F%2826%29
x+=+%28-54+%2B-+sqrt%28+576+%29%29%2F%2826%29
x+=+%28-54+%2B-+24%29%2F%2826%29
x+=+%28-27+%2B-+12%29%2F%2813%29
[3] x+=+-15%2F13
[4] x+=+-3
substitute [3] in [2]
y+=+-15%2F13+%2B+3
y+=+-15%2F13+%2B+39%2F13
y+=+24%2F13
[5] (-15/13 , 24/13) is one solution
substitute [4] in [2]
y+=+-3+%2B+3
y+=+0
[6] (-3 , 0) is the other solution
check [5] in [1]
4%2A%28-15%2F13%29%5E2+%2B+9%2A%2824%2F13%29%5E2=+36
4%2A%28-15%2F13%29%5E2+%2B+9%2A%2824%2F13%29%5E2=+36
Multiply both sides by 13^2
4%2A%28-15%29%5E2+%2B+9%2A%2824%29%5E2=+36+%2A+13%5E2
4+%2A+225+%2B+9+%2A+576+=+6084
900+%2B+5184+=+6084
6084+=+6084
OK
check [6] in [1]
4%2A%28-3%29%5E2+%2B+9%2A%280%29%5E2=+36
4+%2A+9+%2B+0+=+36
36+=+36
OK