Get Step-by-Step Solutions to Systems of Equations

High School
Algebra
Algebra I
Systems of equations

Recent questions in Systems of equations

dripcima24 2022-09-29

If A is a matrix, and the system AX=O has a non-trivial solution, show that there is no matrix, B, such that BA=I.

misyjny76 2022-09-27

You have an 24 cm long string. Examine if you can cut in two parts and create
a) Two squares
b) Two circles
whose total area is 20 cm $^{2}$ . (The entire length must be used)
It says the string is cut into 2 parts, and not 2 equal parts.
So for 2 squares: The sum of perimeters will be 24 cm. That's,
$4 l_{1} + 4 l_{2} = 24$ and $l_{1}^{2} + l_{2}^{2} = 20$
Similarly, For 2 circles:
$2 π r_{1} + 2 π r_{2} = 24$ and $π r_{1}^{2} + π r_{2}^{2} = 20$
I get 2 equations and 2 unknowns, how do I solve these equations?

Darius Miles 2022-09-26

Initial value problem with a delta term
${\begin{cases} x^{'} = 3 x - y + δ (t - 1) \\ y^{'} = x + y \end{cases}$
$x (0) = y (0) = 1$

easternerjx 2022-09-26

How to solve a system of two linear equations with two unknowns?
${\begin{cases} 7 (a + b) = b - a \\ 4 (3 a + 2 b) = b - 8 \end{cases}$

Stacy Barr 2022-09-26

Perimeter =48 m
Let the length be 𝑥 m and the breadth be 𝑦 m
As we know, Perimeter =2(𝑥+𝑦)=48 $\Rightarrow x + y = 24$ 𝑥+𝑦=24 [⋯(1)]
Area=135 m $^{2}$ .
As we know, Area=𝑙𝑏
Therefore, 135 m $^{2}$ =𝑥𝑦 [⋯(2)]

Liberty Page 2022-09-25

How to use differential equations to write $x (t)$ in terms of $y$ and $y_{0}$ ?
${\begin{array}{rcrcl} x^{'} & = & - a x & + & b x y \\ y^{'} & = & c y & - & d x y \end{array}$

Ivan Buckley 2022-09-23

Solve the linear system by Gaussian elimination
${\begin{cases} - 2 b + 3 c = 1 \\ 3 a + 6 b - 3 c = - 2 \\ 6 a + 6 b + 3 c = 5 \end{cases}$
An inconsistent linear system with the third row being 0 0 0 6?

Colten Andrade 2022-09-23

Given
$X = \frac{a + \frac{1}{2} b}{a + b + c}$
$Y = \frac{b (\frac{\sqrt{3}}{2})}{a + b + c}$
$Z = \frac{76 a + 150 b + 29 c}{255}$
in other words How do i get $a$ , $b$ , and $c$ on the left side using these three formulas?

hommequidort0h 2022-09-23

Mr. and Mrs. Ahuja weigh 𝑥 kg and 𝑦 kg respectively. They both take a dieting course at the end of which Mr. Ahuja loses 5 kg and weighs as much as the wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs 7/8th of what her husband weighed before the course. From two equations in 𝑥 and 𝑦 and hence find their present weights.

Linda Peters 2022-09-23

Find all triplets $(x, y, z)$ that satisfy:
$x^{2012} + y^{2012} + z^{2012} = 3 x^{2013} + y^{2013} + z^{2013} = 3 x^{2014} + y^{2014} + z^{2014} = 3$
Trivial solution: $(1, 1, 1)$

besnuffelfo 2022-09-23

For which real values of t does the following system of linear equations:
${\begin{matrix} t x_{1} + x_{2} + x_{3} = 1 \\ x_{1} + t x_{2} + x_{3} = 1 \\ x_{1} + x_{2} + t x_{3} = 1 \end{matrix}$
Have:
a) a unique solution?
b) infinitely many solutions?
c) no solutions?

Stacy Barr 2022-09-22

y=(20x+3)r+x and y is 50. What is x and r values?

Elias Heath 2022-09-22

In a parallelogram, one angle is $2 / 5 t h$ of the adjacent angles. Determine the angles of the parallelogram.
Let the adjacent angles be $2 x$
Let the other angle be $y$
Accordingly, $y = 6 / 5 * 2 x$
What is next?

David Ali 2022-09-20

Find answers of this system of equations in reals
${\begin{matrix} x + 3 y = 4 y^{3} \\ y + 3 z = 4 z^{3} \\ z + 3 x = 4 x^{3} \end{matrix}$

Khalfanebw 2022-09-20

Given:
$\begin{matrix} (1) & A = [\begin{matrix} q_{1} & q_{2} & q_{3} \\ q_{4} & q_{5} & q_{6} \\ q_{7} & q_{8} & q_{9} \end{matrix}] \end{matrix}$
$A$ is a matrix with determinant 1,orthogonal , invertible and not necessary that all $q_{i}$ s are equal. All entries of the A are constants cant alter
$\begin{matrix} (2) & C = [\begin{matrix} p_{1} & p_{2} & p_{3} \\ p_{4} & p_{5} & p_{6} \\ p_{7} & p_{8} & p_{9} \end{matrix}] \end{matrix}$
$C$ is a matrix which is non-invertible and not necessary that all $p_{i}$ s are equal. All entries of the $C$ are constants cant alter
$\begin{matrix} (3) & B = (\begin{array}{ccc} 0 & - z & y \\ z & 0 & - x \\ - y & x & 0 \end{array}) \end{matrix}$
$B$ is a matrix which is non-invertible. It is the varible matrix,and the variables are $x, y, z$
If we have the equation
$\begin{matrix} (4) & A = B C \end{matrix}$
Can we find the solutions of $x, y, z$ interms of constants $p_{i}$ s and $q_{i}$ s ?

Kaila Branch 2022-09-20

Find homogeneous system of linear equations whose solution space is: V = span((1,-2,4,3),(1,-1,6,4),(3,-8,8,3)).
First I found vectors were linearly dependent, so I discarded the third vector to form a new base. Next I figured system will have 2 free variables and if we would use gauss-jordan elimination on matrix of a system we would get this:
$[\begin{matrix} 1 & 0 & * & * \\ 0 & 1 & * & * \end{matrix}]$

kayleenicholemaynard 2022-09-19

find an equation of the line described below. write the equation in slope-intercept form when possible:
through (8,6) and (6,8)

Mainuillato2p 2022-09-19

If Sue buys A, she will have $1.50 left; if she buys B, she will have $2 left. Given that 2A=3B, how much money does she have?

gemauert79 2022-09-18

Determine the value for k for which the system of linear equation has infinitely many solution.
${\begin{cases} 2 x - y = 2 \\ 4 x + k y = 4 \end{cases}$

honigtropfenvi 2022-09-17

Finding the value of a variable present in two functions
$k x - 3 and x^{2} + k$

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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