# Tagged Questions

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### what would be the way to solve a system of equations like this one?

Solve: $xy=-30$ $x+y=13$ {15, -2} is a particular solution, but, how would I know if is the only solution, or what would be the way to solve this without "guessing" ?
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### How to solve the following pair of equation.

The pair of equation I need to solve is $x^2+12x+y^2-4y=24$ $x^2-6x+y^2+8y=25$ I have no idea on how to do these kinds of problems (may be by elimination?)
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### Consider the following simultaneous equations in $x$ and $y$…where $a$ is a real constant: $x+y+axy=a$,$x-2y-xy^2$

Consider the following simultaneous equations in $x$ and $y$: $$x+y+axy=a$$ $$x-2y-xy^2=0$$ where $a$ is a real constant. Show that these equations admit real solutions in $x$ and $y$. I could not ...
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### Three variable systems if equations.

Given the quadratic function $y=x^2 + 4$ and the linear function $y=x + b$, determine all the possible values of $b$ that would result in a system if equations with two solutions, exactly one ...
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### $x^2+y^2=1, 5x+12y+13=0$ Simultaneous Equations

Can someone solve this for me and show working out? I just can't do it and I don't know why I am getting x and y wrong. It will be very much appreciated. As basic as possible as well please.
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### Symmetric System of Equations

I'm new on studying Systems of equations. I just want to know the number of real solutions of this system of equations: \begin{align*} x^2-y^2=z\\ y^2-z^2=x\\ z^2-x^2=y \end{align*} I also want to ...
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### Solving system of multivariable 2nd-degree polynomials

How would you go about solving a problem such as: \begin{matrix} { x }^{ 2 }+3xy-9=0 \quad(1)\\ 2{ y }^{ 2 }-4xy+5=0 \quad(2) \end{matrix} where $(x,y)\in\mathbb{C}^{2}$. More generally, how would ...
### Solve $5a^2 - 4ab - b^2 + 9 = 0$, $- 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0$
Solve $\left\{\begin{matrix} 5a^2 - 4ab - b^2 + 9 = 0\\ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0. \end{matrix}\right.$ I know that we can use quadratic equation twice, but then we'll get some ...