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What are the solutions to the simultaneous equations of 3x -2y equals 1 and 3x squared -2y squared plus 5 equals 0 showing work 1?
Wiki User
∙ 7y ago
1st equation: 3x-2y = 1 or 3x = 1+2y
2nd equation: 3x^2 -2y^2 +5 = 0 or 3x^2 = 2y^2 -5
Square both sides in 1st equation and multiply all terms in 2nd equation by 3
If: 9x^2 = 1+4y+4y^2 and 9x^2 = 6y^2 -15
Then: 6y^2 -15 = 1+4y+4y^2 => 2y^2 -4y-16 = 0
Dividing all terms by two: y^2 -2y-8 = 0
Factorizing: (y-4)(y+2) = 0 => y = 4 or y = -2
Solutions by substitution: x = 3 and y = 4 or x = -1 and y = -2
Wiki User
∙ 7y ago
Wiki User
∙ 7y ago3x - 2y = 1=> 2y = 3x - 1 => y = (3x - 1)/2
3x^2 - 2y^2 + 5 = 0
=> 3x^2 - 2[(3x - 1)/2]^2 + 5 = 0
=> 3x^2 - 2*[(9*x^2 - 6x + 1)/4)] + 5 = 0
=> 3x^2 - (9*x^2 - 6x + 1)/2) + 5 = 0
=> 3x^2 - 9/2*x^2 + 3x - 1/2 + 5 = 0
=> -3/2x^2 + 3x + 9/2 = 0
=> 3x^2 - 6x - 9 = 0
=> x^2 - 2x - 3 = 0
=> (x + 1)*(x - 3) = 0
=> x = -1 or x = 3
x = -1 => y = [3*(-1) - 1]2 = -4/2 = -2
and
x = 3 => y = [3*3 - 1]/2 = 8/2 = 4
So the solutions are: (-1, -2) and (3, 4).
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What are the solutions to the simultaneous equations of x -2y equals 1 and 3xy -y squared equals 8 showing all appropiate work with answers?
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What are the solutions to the simultaneous equations of x -2y equals 1 and 3xy -y squared equals 8?
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What are the solutions of the simultaneous equations of x squared -xy -y squared equals -11 and 2x plus y equals 1?
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What are the solutions to the simultaneous equations of x equals 2y -2 and x squared equals y squared plus 7 showing work?
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