# Questions tagged [systems-of-equations]

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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### Finding real $(x,y)$ solutions that satisfies a system of equation.

I was given: $x + y^2 = y^3 ...(i) \\ y + x^2 = x^3...(ii)$ And was asked to find real $(x,y)$ solutions that satisfy the equation. I substracted $(i)$ by $(ii)$: $x^3 - y^3 + y^2 - x^2 + x - y = 0$ ...
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### Geometric sequence problem including sum of the numbers

Numbers: $a,b,c,d$ generate geometric sequence and $a+b+c+d=-40.$ Find these numbers if $a^2+b^2+c^2+d^2=3280$ I tried this problem and I have system of equations which I can't solve. I think there ...
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### How to solve these two equations together to get an expression for $V_{OUT}$ and $I_{DS}$ [closed]

$$I_{DS} = \frac{K}{2} (V_{IN} - V_{OUT} - V_T)^2$$ $$V_{OUT} = I_{DS} R_S$$ I have these two equations which I want to solve simultaneously to get an expression for $I_{DS}$ in terms of $V_{IN}$, $K$...
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### Closed Form Solution to System of Equations

Let $\mathbf{b} \in \mathbb{R}_+^n$, $\mathbf{V} \in \mathbb{R}_+^{n \times m}$ with $\mathbf{V} \mathbf{1}_m = \mathbf{1}_n$ where $\mathbf{1}_n$ is the vector of ones of size $n$. I have the ...
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### How to compute values of variables of a system of equations? [closed]

I have some equations which relate to each other and these are down below $z+p=12.78248$ $a+x=2.16943$ $z+2a=11.75629$ $p+2x=5.36505$ I am trying to figure out a numerical value of any one variable ...
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### Solving system of equations with three unknowns

I need to solve an equation of a line using three known coordinate pairs (x0, y0), (x1, y1), and (x2, y2). The equation of the plane is, of course, ax + by + c = 0. I'm writing a little piece of code ...
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### Trigonometric system for $(0,\pi/2)$

If $x,y,z\in (0,\frac{\pi}2 )$, find all solutions to: $$\begin{cases} \tan x+\sin y+\sin z=3x \\ \sin x+\tan y+\sin z=3y \\ \sin x+\sin y+\tan z=3z\end{cases}$$ Can someone give a hint to me? I can't ...
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### Solving a system of equations, based on a gear, such that solutions are natural numbers or proving no solution exists.

I'm not sure how to exactly ask this question. I'm essentially looking for a way to solve a set of natural numbers from a set of equation based on a gear. In addition I'm looking for a way to prove if ...
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### For the parametric curve whose equation is $x = 4\cos θ$ and $Y = 4\sin θ$, what would be the concavity of curve at θ = π/4?

What I'm actually confused is that I found the slope to be -1 which is correct but when for finding the concavity I take the double derivative of the given function it gives the answer tan π/4 which ...
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### solve equations having term $xy$ [closed]

I want to solve equations: $$x^3-3xy^2=-11$$ and $$y^3-3x^2y=-2$$ for $x$ and $y$. How can I do it?
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### A tricky nonlinear pair of equations [closed]

For example, a question like this. Solve $$\begin{cases} \frac1x+\frac1{2y}&=(x^2 + 3y^2)(3x^2 + y^2) \\ \frac1x-\frac1{2y}&=2(y^4 - x^4) \\ \end{cases}$$ I couldn't see any way to approach ...
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### solve $x_1'(t) =x_1 (t) + 2x_2(t) , x_2'(t)=2x_1(t)+4x_2(t)$

I have found eigenvalues and eigenvectors, but I have no idea what to do next. How do I find x with them?
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### Solving Modular System with 2 different Moduli

Is there any way to solve for $a$ and $b$ in: $$a*b \equiv s_0 \mod r_0$$ $$a - b - a*b \equiv s_1 \mod ( r_0 - 1)$$ I have the values of $r_0$, $s_0$, $s_1$ and would ...
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### Proving Linearly Independence from System of Equation

I am trying to understand the proof of Linearly Independence of the basis set $\{1, x, x^2, x^3\}$. It is written that - Substituting $3$ other values of $x$ into the above equation yields a system ...
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### Need help in solving a linear algebra ( System of Equations) quiz problem

I am solving previous year quiz problem of my class and I am unable to solve this question in linear algebra. Let $A \in M_{m \times n}(\Bbb{R})$ and let $b_0 \in \Bbb{R}^m$. Suppose the system of ...
It is given on pg. #106, 107 in the book by: Thomas Banchoff, John Wermer; titled: Linear Algebra Through Geometry, second edn.. Consider a system of two equations in three unknowns: a_1x_1 + a_2x_2 ...