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High School
Algebra
Algebra I
Systems of equations

Recent questions in Systems of equations

woowheedr 2022-07-06

1.) Given the following equations:
$3 x - y = 30 5 x - 3 y = 10$
What are the values of $x$ and $y$ ?

Gauge Terrell 2022-07-06

system of three equations
$3 x + y + z = 14$
$- x + 2 y - 3 z = - 9$
$5 x - y + 5 z = 30$

2d3vljtq 2022-07-06

Solve the following system of linear equations for any values of real parameter $a$
${\begin{cases} x + y + 2 z = 1 \\ 2 x + a y - z = 4 \\ 3 x + y + 3 z = 1 \end{cases}$
Calculating the value of determinant I found out, after I equalled it with zero, that $a$ has the value $\frac{- 4}{3}$ . So I thought that if it's required to solve this equation for any $a$ , then first of all I had to suppose that $D = 0$ , this means that $a = \frac{- 4}{3}$ . For this value I found out that there is an infinite number of solutions for this system. But now my question is: what do I have to do with the case when $D \neq 0$ ?

Savanah Boone 2022-07-06

System $a + b + c = 4$ , $a^{2} + b^{2} + c^{2} = 8$ . find all possible values for $c$ .

klipbodok6 2022-07-06

$u + v = 2$
$u x + v y = 1$
$u x^{2} + v y^{2} = - 1$
$u x^{3} + v y^{3} = - 5$
Can anyone give me a hint for solving this ?

gaiaecologicaq2 2022-07-06

finding solution to simultaneous equations when one exists
$\begin{matrix} (1) & 990 = e^{x} \end{matrix}$
$\begin{matrix} (2) & 590 = e^{(x - 10 y)} \end{matrix}$

slijmigrd 2022-07-05

Why does the following nonlinear system have 21 solutions?
$y + x y^{2} - x^{3} + 2 x z^{4} = 0 - x - y^{3} - 3 x^{2} y + 3 y z^{4} = 0 - \frac{5}{2} y^{2} z^{3} - 2 x^{2} z^{3} - \frac{z^{7}}{2} = 0$
there is one real and twenty complex solutions: $(0, 0, 0)$

uri2e4g 2022-07-05

we consider the following model:
${\begin{cases} x^{'} & = x (4 - x - y) \\ y^{'} & = y (2 + 2 α - y - α x) \end{cases}$
a) Find the critical point $P$ does not depend on $α$ and having coordinates strictly positive.
-> The critical points are: $(0, 0), (0, 2 + 2 α), (2, 2), (4, 0)$ then $P = (2, 2)$
b) Assuming $\frac{d y}{d x}$ ,solve the system for the value $α_{0}$ of $α$ and such that $P$ is not hyperbolic,
Draw the phase portrait for $α = α_{0}$
c) what is the nature of $P$ for $0 < α < α_{0}$ and $α_{0} < α$ , Draw the shape of the phase portraits for these values of $α$
Can someone tell me how to solve b), why they use $\frac{d y}{d x}$ ?

Jorden Pace 2022-07-04

How to frame this set of linear equations?
$2 x + 1 y + 2 z = A$
$0 x + 2 y + 2 z = A$
$1 x + 2 y + 1 z = A$
I assume this can be rewritten as a matrix? How can I check if a solution exists such that x, y, and z are nonnegative?

Joshua Foley 2022-07-04

Consider the system of equations in real numbers $x, y, z$ satisfying
$\frac{x}{4 \sqrt{x^{2} + 1}} = \frac{y}{5 \sqrt{y^{2} + 1}} = \frac{z}{6 \sqrt{z^{2} + 1}}$
and $x + y + z = x y z$ . Find $x, y, z .$ .
I substituted $x, y, z$ as $\tan (θ_{1}), \tan (θ_{2}), \tan (θ_{3})$ , where
$θ_{1} + θ_{2} + θ_{3} = 180 º .$

tripes3h 2022-07-04

Finding general solution for a nonhomogeneous system of equations
${\begin{cases} x_{1}^{'} = x_{2} + 2 e^{t} \\ x_{2}^{'} = x_{1} + t^{2} \end{cases}$
I want to find the general solution for it. I started by finding the general solution for the homogeneous equations:
$(\begin{matrix} x_{1} \\ x_{2} \end{matrix}) = C_{1} (\begin{matrix} e^{t} + e^{- t} \\ e^{t} - e^{- t} \end{matrix}) + C_{2} (\begin{matrix} e^{t} - e^{- t} \\ e^{t} + e^{- t} \end{matrix})$
Now I need to find a "specific" solution for the nonhomogeneous equations but I have problems applying the method in which I make constants $C_{1}$ and $C_{2}$ a variable.

Ellie Benjamin 2022-07-04

Find solution for the following system:
$x^{'} = y^{3} - 4 x$ , $y^{'} = y^{3} - y - 3 x$
As I found the three equilibrium points, $(0, 0)$ , $(- 2, - 2)$ , $(2, 2)$
how to find the solution for this one since they are not fully decoupled or partially decoupled?

Montenovofe 2022-07-03

How would you solve the following system of equations:
$x^{2} + y = 4 x + y^{2} = 10$
I tried defining y in terms of x and then inserting in to the second equation:
$y = 4 - x^{2} x + (4 - x^{2})^{2} = 10$
Expand the second equation:
$x + 16 - 8 x^{2} + x^{4} = 10$
Rearrange the terms:
$x^{4} - 8 x^{2} + x + 6 = 0$

kreamykraka80 2022-07-03

Solving a system in 3 variables problem
Find $x$ , $y$ , and $z$ from the problem below.
$\begin{array}{rcl} - 2 x + 1 & = & 5 \\ 2 x + 3 y - 4 z & = & 7 \\ 3 x + 2 y + 2 z & = & 3 \end{array}$

Cierra Castillo 2022-07-03

How find this linear equation
let $a \in R$ ,then solve this follow equation:
${\begin{cases} x_{1} - x_{2} - x_{3} - \dots - x_{n} = 2 a \\ - x_{1} + 3 x_{2} - x_{3} - \dots - x_{n} = 4 a \\ - x_{1} - x_{2} + 7 x_{3} - \dots - x_{n} = 8 a \\ \dots \dots \dots \dots \dots \dots \\ - x_{1} - x_{2} - x_{3} - \dots + (2^{n} - 1) x_{n} = 2^{n} a \end{cases}$

pipantasi4 2022-07-03

Consider the system
$x^{'} = \frac{- x}{2}; y^{'} = 2 y + x^{2}$
Show that this system is topologically conjugate to the linear system $D F_{(0, 0)}$
a) Solve both the linear and nonlinear systems and express your answers as a flows $ϕ_{t}^{L} (x, y)$ and $ϕ_{t}^{N} (x, y)$ respectively.
b) As I found $ϕ_{t}^{L} (x_{0}, y_{0})$ = $(x_{0} e^{\frac{- 1}{2} t}, y_{0} e^{2 t})$ and $ϕ_{t}^{N} (x_{0}, y_{0})$ = $(x_{0} e^{\frac{- 1}{2} t}, (y_{0} + \frac{1}{3} x_{0}^{2}) e^{2 t} - \frac{x_{0}^{2}}{3} e^{- t})$ Do they look right to you?
c) Find the topological conjugacy that maps the flow of the nonlinear system to that of the linear system.

Dayanara Terry 2022-07-03

How to solve system equation
${\begin{matrix} x^{3} + y^{3} + z^{3} = x + y + z \\ x^{2} + y^{2} + z^{2} = x y z \end{matrix}$
$x, y, z \in R$

racodelitusmn 2022-07-03

Solve the following system of differential equations
$\begin{aligned} \dot{x} & = 2000 - 3 x y - 2 x \\ \dot{y} & = 3 x y - 6 y \\ \dot{z} & = 4 y - 2 z \end{aligned}$

Sylvia Byrd 2022-07-03

System of linear equations dependent on $a$ :
$x + y + z = 1$
$- 2 x + 2 y + a z = 3$
$- a x + y + 2 z = 2$
I'm transforming this to a matrix.
$M_{1} = [\begin{array}{cccc} 1 & 1 & 1 & 1 \\ - 2 & 2 & a & 3 \\ - a & 1 & 2 & 2 \end{array}]$
I'm switching $x$ with $y$ column and sort.
$M_{2} = [\begin{array}{cccc} 1 & 1 & 1 & 1 \\ 1 & - a & 2 & 3 \\ 2 & - 2 & a & 2 \end{array}]$
Solving this:
$M_{3} = [\begin{array}{cccc} 1 & 1 & 1 & 1 \\ 0 & - a - 1 & 1 & 2 \\ 0 & 0 & a + 2 & 5 \end{array}]$
Therefore I'm getting
$a = 3$
Putting it into the $M 1$ yields no result, as I end up with.
$M = [\begin{array}{cccc} 1 & 1 & 1 & 1 \\ 0 & 4 & 5 & 1 \\ 0 & 4 & 5 & 5 \end{array}]$
Is there an error in my calculation?

kolutastmr 2022-07-02

Logarithmic system of equations
$\begin{aligned} \ln (x) & = 3 \ln (y) \\ 3^{x} & = 27^{y} \end{aligned}$

In simple terms, systems of equations represent a special set of simultaneous equations where the equation system is used as a finite element. The trick here is to find common solutions, which is exactly what systems of equations solver must achieve. If this does not sound clear to you, take a look at some systems of equations answers below and see those with explanations. The solution will always come in three variables (namely, x, y, and z), which will represent your ordered triple. See systems of equations solutions for more examples of how it works in practice.

Algebra I

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