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High School
Algebra
Algebra I
Systems of equations

Recent questions in Systems of equations

przesypkai4 2022-07-27

How many Gallons of a 12% indicator solution must be mixed with a20% indecator solution to get 10 gallons of a 14% solution.

Lexi Mcneil 2022-07-27

Find the value of such that the system of equations.
-9x+ky=5 6x+10y=7

Elsa Brewer 2022-07-26

Let $A = [\begin{matrix} 1 & - 3 & - 4 \\ - 3 & 2 & 6 \\ 5 & - 1 & - 8 \end{matrix}] and \vec{b} = [\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \end{matrix}]$
Show that the equation Ax=b does not have a solution for all possible b, anddescribe the set of all b for which Ax=b does have a solution.
Please explain in steps and especially the finall step towhere you explain for which values b does have a solution and whenthere is none.

Nash Frank 2022-07-26

A rancher buys 100 live animals for $100. Chickens cost 50 cents each, goats cost $3.50 each, and cows cost $10 each. How many of each did the rancher buy?

Noelanijd 2022-07-24

Solve the following system of equations by using the inverse of the coefficient matrix A. (AX = B) x + 5y= - 10, -2x+7y=-31

lilmoore11p8 2022-07-16

How can I show that there are only finitely many solutions for the following system?
$x^{2} + y z = x$
$y^{2} + z x = y$
$z^{2} + x y = z$

myntfalskj4 2022-07-16

Suppose that I have an image with $n$ pixels and the following equation,
$\sum_{r \in P} (U (r) - \sum_{s \in N (r)} w_{r s} U (s))^{2} = 0$
$U = (U (1), U (2), . . ., U (n))$ are the variables;
$P$ is the set of all the $n$ pixels;
$N (r)$ is the set of all neighboring pixels of $r$ . For example, for an image with $3 \times 3$ pixels, $N (1) = {2, 4, 5}$
$w_{r s}$ is a weighting function where $\sum_{s \in N (r)} w_{r s} = 1$
Note: I just mentioned that it is an image to better explain the role of the set $N$ and the function $w_{r s}$ .
Well, it's easy to show that "one" solution for that equation are the scalar multiples of the all-ones vector. I mean, $U = k \cdot (1, 1, . . ., 1)$ is clearly a solution.
My question is: there's a way to proof that this is the "only" solution for the above equation?

grenivkah3z 2022-07-15

Consider the two equations below:
$y_{1} = (1 - \frac{a_{1}}{x}) e^{- \frac{α a_{1}}{x}} y_{2} = (1 - \frac{a_{2}}{x}) e^{- \frac{α a_{2}}{x}}$
Given $y_{1}$ , $y_{2}$ , $a_{1}$ and $a_{2}$ , is there an analytical way to determine $α$ and $x$ ?

Raul Walker 2022-07-15

How to solve systems of equations with multiplication & addition.
$a + b = 12$
$a \cdot b = 36$

Augustus Acevedo 2022-07-15

How to solve this coupled 2nd order Differential equation of a double pendulum- Runge Kutta method
$θ_{1}^{″} = \frac{- g (2 m_{1} + m_{2}) s i n θ_{1} - m_{2} g s i n (θ_{1} - 2 θ_{2}) - 2 s i n (θ_{1} - θ_{2}) m_{2} (θ_{2}^{' 2} l_{2} + θ_{1}^{' 2} l_{1} c o s (θ_{1} - θ_{2})}{l_{1} (2 m_{1} + m_{2} - m_{2} c o s (2 c o s (2 θ_{1} - 2 θ_{2})))}$
$θ_{2}^{″} = \frac{2 s i n (θ_{1} - θ_{2}) (θ_{1}^{'} l_{1} (m_{1} + m_{2}) + g (m_{1} + m_{2}) c o s θ_{1} + θ_{2}^{' 2} l_{2} m_{2} c o s (θ_{1} - θ_{2}))}{l_{2} (2 m_{1} + m_{2} - m_{2} c o s (2 c o s (2 θ_{1} - 2 θ_{2})))}$
These are the equations, and How can I possibly solve this simultaneoouslt in RK4 method?
$m_{1}, m_{2} =$ =masses of pendulum 1 and 2, $θ_{1}, θ_{2} =$ = angles formed by the pendulums, $θ_{1}^{'} = ω_{1}, θ_{2}^{'} = ω_{2}$

Kristen Stokes 2022-07-14

Simultaneous solution(s) to
$a^{2} + 4 b^{2} + 4 a b = 0 a^{2} + 4 b^{2} + 32 + 16 a - 8 b = 0$

Bruno Pittman 2022-07-13

For the system
${\begin{array}{rcrcrcr} x & + & 3 y & - & z & = & - 4 \\ 4 x & - & y & + & 2 z & = & 3 \\ 2 x & - & y & - & 3 z & = & 1 \end{array}$
what is the condition to determine if there is no solution or unique solution or infinite solution?

Ellie Benjamin 2022-07-13

If
1. $a + b + c = 4$
2. $a^{2} = b^{2} + c = 6$ (this is not symmetric equation)
3. $a^{3} + b^{3} + c^{3} = 8$
Then find the value of $a^{4} + b^{4} + c^{4}$

kolutastmr 2022-07-13

Find the real numbers a,b,c,d,e in [−2,2] that simultaneously satisfy the following relations:
$a + b + c + d + e = 0$
$a^{3} + b^{3} + c^{3} + d^{3} + e^{3} = 0$
$a^{5} + b^{5} + c^{5} + d^{5} + e^{5} = 10$

Lorena Beard 2022-07-12

How to solve this this equations?
$- 555 = 0.862 X + 0.138 Y - 0.345 Z, - 911 = 0.413 X + 0.587 Y - 0.492 Z, 674 = 0.849 X + 0.142 Y + 0.358 Z,$

doturitip9 2022-07-12

Solving a system of equations $x - y = 17$ , $\frac{4}{3} x + \frac{3}{2} y = 0$

hornejada1c 2022-07-12

$a b + a + b = 250$
$b c + b + c = 300$
$a c + a + c = 216$
then find $a + b + c = ?$

daktielti 2022-07-12

Question: For the value(s) of $k$ , if any, will the following system have (a) no solution, (b) a unique solution, (c) infinity many solutons:
$x + y + k z = 1, x + k y + z = 1, x k + y + z = - 2.$

hornejada1c 2022-07-11

Consider
$y^{″} + y = 2 x \sin (x)$
I have the solution for the homogeneous equation. Now i am trying to guess a particular solution for: $2 x \sin (x)$
My first guess was: $(A x + B) \cos x + (C x + D) \sin x$ but i end up with the system:
${\begin{matrix} - 2 A & + 2 B & = 0 \\ 2 C = 0 \end{matrix}$
Then my quess was: $(A x^{2} + x B) \cos x + (C x^{2} + x D) \sin x$ but that leaves me with:
${\begin{matrix} - A x & - B & + 4 C & = 0 \\ 2 A & 2 D & = 0 \\ - 4 A & - C x & - D & = 0 \\ - 2 B & 2 C & = 0 \end{matrix}$
Is here something wrong?

hryggcx 2022-07-11

Sum of cubed roots
$x_{1}^{3} + x_{2}^{3} + x_{3}^{3}$
$x_{1}^{4} + x_{2}^{4} + x_{3}^{4}$
where $x_{1}, x_{2}, x_{3}$ are the roots of
$x^{3} + 2 x^{2} + 3 x + 4 = 0$
using Viete's formulas.
I know that $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} = - 2$ , as I already calculated that, but I can't seem to get the cube of the roots. I've tried
$(x_{1}^{2} + x_{2}^{2} + x_{3}^{2}) (x_{1} + x_{2} + x_{3})$
but that did work.

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

Strengthen Your Systems of Equations Skills