10
votes
6answers
1k views

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" ?
0
votes
2answers
39 views

Can one solve this system of qudratic equations unambigiously?

Given the parameters $p_1, p_2, p_3$ I want to know if the following system can be solved: $p_1 a + p_2 c + ef = 0\\ p_1 b + cd + p_3 f = 0\\ ab + p_2 d + p_3 f = 0\\ p_1^2 +a^2+b^2=1\\ ...
2
votes
5answers
72 views

Algebraic process to find numbers so that $xy=45$ and $x+y=18$

Can someone help me with the following question? The sum of two numbers is $18$ and their product is $45$. Find the numbers. I know that the answer is $15$ and $3$. But how do I find that answer ...
0
votes
0answers
20 views

system of two quadratic equations with two variables

Is there a general way to solve exactly a system of this shape (the $a_i$ are constants): $$\begin{array}{cc}a_1x^2+a_2x+a_3y^2+a_4y+a_5=0\\ a_6xy+a_7x+a_8y+a_9=0 \end{array} $$ It comes from a ...
0
votes
1answer
18 views

system of equations solving with only that information

Hi would would I go around to solve the following, there is no other information stat is given other than the fact that i have already expanded this from this $(25-y)(x+8)=523$ $25x-8y=323$
-1
votes
2answers
47 views

Proof of axis of symmetry equation [closed]

Because quadratic functions are symmetrical how do you prove the axis of symmetry equation. $x=(-b/(2a))$
1
vote
1answer
79 views

Solve …

This is what I did Can anyone tell me what's wrong me or the question?
3
votes
1answer
36 views

Problem with system of equations

I wonder how to solve this system of equations: $\begin{cases} 2x^2+y^2=43\\2x^2+4xy=78\end{cases}$ when I subtract I have $y(4x-y)=35$ but I don't if it is good way to look for the solutions.
0
votes
1answer
90 views

Solve a bit tricky system of equations

I want to solve the system for $x$, $y$ and $z$. Is there any smart trick to solve it? $$\begin{cases} 2a(ax+by)+2c(cx+dy)+2zx=0 \\ 2b(ax+by)+2d(cx+dy)+2zy=0 \\ x^2+y^2-1=0\end{cases}$$ $a,b,c,d \in ...
2
votes
2answers
64 views

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?)
1
vote
1answer
21 views

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 ...
1
vote
2answers
39 views

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 ...
0
votes
4answers
71 views

$x^2+y^2=1, 5x+12y+13=0$ 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.
-1
votes
1answer
380 views

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 ...
4
votes
2answers
185 views

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 ...
1
vote
2answers
114 views

System of quadratic equations

How would you solve the following system of equations: $$ x^2 + y = 4 \\ x + y^2 = 10 $$ Thanks very much! I tried defining y in terms of x and then inserting in to the second equation: $$ y = 4 - ...
0
votes
0answers
295 views

If $ a+b+c=4 ; a^2=b^2+c=6 ; a^3+b^3+c^3=8 $ Then find the value of $a^4+b^4+c^4$

If $a+b+c=4$ $ a^2=b^2+c=6$ (this is not symmetric equation) $a^3+b^3+c^3=8$ Then find the value of $a^4+b^4+c^4$
3
votes
3answers
169 views

Systems of Quadratic Equations Question

looking for help on this question. Solve the following systems of equations algebraically using the quadratic formula. $$\begin{align} y& =-x^2+2x+9\\ y& =-5x^2+10x+12\end{align}$$ Any help ...
0
votes
5answers
336 views

How to solve systems of equations with multiplication & addition.

So I have a system of equations: $$a + b = 12$$ $$a \cdot b = 36$$ In this case, $a$ and $b$ are both $6$, this can be easily done in your head. However, how can you scale this for larger problems?
7
votes
6answers
365 views

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 ...