SOLUTION: Solve the simultaneous equation. {{{2x + 3y = 13}}} {{{2xy + 5y^2 - 4x^2 = 41}}}

Algebra ->  Equations -> SOLUTION: Solve the simultaneous equation. {{{2x + 3y = 13}}} {{{2xy + 5y^2 - 4x^2 = 41}}}       Log On


   

Question 833257: Solve the simultaneous equation.
2x+%2B+3y+=+13
2xy+%2B+5y%5E2+-+4x%5E2+=+41
Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

1.2x+%2B+3y+=+13
2.2xy+%2B+5y%5E2+-+4x%5E2+=+41
From eq. 1,
2x=13-3y
Substitute,
2xy+%2B+5y%5E2+-+4x%5E2+=+41
2xy+%2B+5y%5E2+-+%282x%29%5E2+=+41
%2813-3y%29y%2B5y%5E2-%2813-3y%29%5E2=41
13y-3y%5E2%2B5y%5E2-%289y%5E2-78y%2B169%29=41
%28-3%2B5-9%29y%5E2%2B%2813%2B78%29y-169=41
-7y%5E2%2B91y-210=0
y%5E2-13y%2B30=0
%28y-3%29%28y-10%29=0
Two solutions:
y-3=0
y=3
Then from eq. 1,
2x=13-3%283%29
2x=13-9
2x=4
x=2
.
.
.
y-10=0
y=10
2x=13-3%2810%29
2x=13-30
x=-17%2F2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the simultaneous equation.
2x+%2B+3y+=+13
2xy+%2B+5y%5E2+-+4x%5E2+=+41
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2x+%2B+3y+=+13 --> 2x = 13 - 3y
2xy+%2B+5y%5E2+-+4x%5E2+=+41
Sub for 2x in the 2nd eqn
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%2813-3y%29%2Ay+%2B+5y%5E2+-+%2813-3y%29%5E2+=+41
-3y%5E2+%2B+13y+%2B+5y%5E2+-+169%2B78y-9y%5E2+=+41
-7y%5E2++%2B+91y+-210+=+0
y%5E2+-+13y+%2B+30+=+0
y = 3, 10
Sub for y in the 1st eqn to find x