Recent questions in Systems of equations

Algebra IAnswered question

Elias Hardy 2023-03-23

The weight of a bicycle is 7 kg 450 g. What is the weight of the bicycle in grams?

A. 7,450 g

B. 7,600 g

C. 7,810 g

D. 7,920 g

A. 7,450 g

B. 7,600 g

C. 7,810 g

D. 7,920 g

Algebra IAnswered question

odveza6ad 2023-03-06

How to solve the system of equations $3x+2y=14$ and $y=x+2$ by substitution?

Algebra IAnswered question

xcopyv4n 2023-02-28

Determine the value of k so that the following linear equations have no solution:$(3k+1)x+3y-2=0\phantom{\rule{0ex}{0ex}}({k}^{2}+1)x+(k-2)y-5=0$

Algebra IAnswered question

osadczyttq 2023-01-30

There are multiple chickens and rabbits in a cage. There are 72 heads and 200 feet inside of the cage. How many chickens and rabbits are in there?

Algebra IAnswered question

Taniyah Hartman 2022-12-30

How to solve this system of equations: $y={x}^{2}+4x-2;y=2x+1$ ?

Algebra IAnswered question

adailymonthly7ve 2022-12-19

The system of equations sim, find missing

4x+5y=8

8x +_y=_

4x+5y=8

8x +_y=_

Algebra IAnswered question

n3g2r46z 2022-12-17

Which of the systems of equations below could not be used to solve the following system for x and y? $\{\begin{array}{l}6x+4y=24\\ -2x+4y=-10\end{array}$

A. $\{\begin{array}{l}6x+4y=24\\ 2x-4y=10\end{array}$

B. $\{\begin{array}{l}6x+4y=24\\ -4x+8y=-20\end{array}$

C. $\{\begin{array}{l}18x+12y=72\\ -6x+12y=-30\end{array}$

D. $\{\begin{array}{l}12x+8y=48\\ -4x+8y=-10\end{array}$

A. $\{\begin{array}{l}6x+4y=24\\ 2x-4y=10\end{array}$

B. $\{\begin{array}{l}6x+4y=24\\ -4x+8y=-20\end{array}$

C. $\{\begin{array}{l}18x+12y=72\\ -6x+12y=-30\end{array}$

D. $\{\begin{array}{l}12x+8y=48\\ -4x+8y=-10\end{array}$

Algebra IAnswered question

RyszardsJh 2022-12-05

BPM interacts through the ________ layer.

A data access

B presentation

C both of options

D none of the above

A data access

B presentation

C both of options

D none of the above

Algebra IAnswered question

Jamir Summers 2022-12-05

To solve a system of equations, you need use substitution. $y=3x-2,y=2x-5$

Algebra IAnswered question

Brenda Leach 2022-11-30

The opposite of squaring a number is division. False or True

Algebra IAnswered question

VarceprewN3M 2022-11-28

Use back substitution to solve each of the following systems of equations:

a) ${x}_{1}-3{x}_{2}=2\phantom{\rule{0ex}{0ex}}2{x}^{2}=6$

b) ${x}_{1}+{x}_{2}+{x}_{3}=8\phantom{\rule{0ex}{0ex}}2{x}_{2}+{x}_{3}=5\phantom{\rule{0ex}{0ex}}3{x}_{3}=9$

c) ${x}_{1}+2{x}_{2}+2{x}_{3}+{x}_{4}=5\phantom{\rule{0ex}{0ex}}3{x}_{2}+{x}_{3}-2{x}_{4}=1\phantom{\rule{0ex}{0ex}}-{x}_{3}+2{x}_{4}=-1\phantom{\rule{0ex}{0ex}}4{x}_{4}=4$

d) ${x}_{1}+{x}_{2}+{x}_{3}+{x}_{4}+{x}_{5}=5\phantom{\rule{0ex}{0ex}}2{x}_{2}+{x}_{3}-2{x}_{4}+{x}_{5}=1\phantom{\rule{0ex}{0ex}}4{x}_{3}+{x}_{4}-2{x}_{5}=1\phantom{\rule{0ex}{0ex}}{x}_{4}-3{x}_{5}=0\phantom{\rule{0ex}{0ex}}2{x}_{5}=2$

Write out the coefficient matrix for each of the systems in first exercise.

a) ${x}_{1}-3{x}_{2}=2\phantom{\rule{0ex}{0ex}}2{x}^{2}=6$

b) ${x}_{1}+{x}_{2}+{x}_{3}=8\phantom{\rule{0ex}{0ex}}2{x}_{2}+{x}_{3}=5\phantom{\rule{0ex}{0ex}}3{x}_{3}=9$

c) ${x}_{1}+2{x}_{2}+2{x}_{3}+{x}_{4}=5\phantom{\rule{0ex}{0ex}}3{x}_{2}+{x}_{3}-2{x}_{4}=1\phantom{\rule{0ex}{0ex}}-{x}_{3}+2{x}_{4}=-1\phantom{\rule{0ex}{0ex}}4{x}_{4}=4$

d) ${x}_{1}+{x}_{2}+{x}_{3}+{x}_{4}+{x}_{5}=5\phantom{\rule{0ex}{0ex}}2{x}_{2}+{x}_{3}-2{x}_{4}+{x}_{5}=1\phantom{\rule{0ex}{0ex}}4{x}_{3}+{x}_{4}-2{x}_{5}=1\phantom{\rule{0ex}{0ex}}{x}_{4}-3{x}_{5}=0\phantom{\rule{0ex}{0ex}}2{x}_{5}=2$

Write out the coefficient matrix for each of the systems in first exercise.

Algebra IAnswered question

Cecilia Wilson 2022-11-25

We have the equation y - 3x = -2

Select true or false

The system of equations has no solution

The system of equations has only one solution

The system of equations has infinitely many solutions

The point (-1,-5) is a solution to the system of equations

The two lines in the system of equations have the same slope

Select true or false

The system of equations has no solution

The system of equations has only one solution

The system of equations has infinitely many solutions

The point (-1,-5) is a solution to the system of equations

The two lines in the system of equations have the same slope

Algebra IAnswered question

Brenda Leach 2022-11-24

Randy has $3.55 worth of dimes and quarters in his pocket. The number of dimes is four more than twice the number of quarters. Which system of equations can be used to find how many dimes (d) and quarters (q) Randy has in his pocket?

Algebra IAnswered question

neudateaLp 2022-11-24

Let $a,b,c$ be nonzero real numbers and let ${a}^{2}-{b}^{2}=bc$ and ${b}^{2}-{c}^{2}=ca$. Prove that ${a}^{2}-{c}^{2}=ab$.

The solution strategy given in the course was to scale the two given equations by $s=\frac{1}{c}$, resulting in ${a}^{2}-{b}^{2}=bc$ becoming ${a}^{2}-{b}^{2}=b$ and ${b}^{2}-{c}^{2}=ca$ becoming ${b}^{2}-1=a$. $c$ is basically being set to 1, but I don't understand the justification. Doesn't scaling by $\frac{1}{c}$ by definition not change the equations, since $(a/c{)}^{2}-(b/c{)}^{2}=(b/c)(c/c)\u27fa{\displaystyle \frac{{a}^{2}-{b}^{2}}{{c}^{2}}}={\displaystyle \frac{bc}{{c}^{2}}}\u27fa{a}^{2}-{b}^{2}=bc$

Where is mistake?

The solution strategy given in the course was to scale the two given equations by $s=\frac{1}{c}$, resulting in ${a}^{2}-{b}^{2}=bc$ becoming ${a}^{2}-{b}^{2}=b$ and ${b}^{2}-{c}^{2}=ca$ becoming ${b}^{2}-1=a$. $c$ is basically being set to 1, but I don't understand the justification. Doesn't scaling by $\frac{1}{c}$ by definition not change the equations, since $(a/c{)}^{2}-(b/c{)}^{2}=(b/c)(c/c)\u27fa{\displaystyle \frac{{a}^{2}-{b}^{2}}{{c}^{2}}}={\displaystyle \frac{bc}{{c}^{2}}}\u27fa{a}^{2}-{b}^{2}=bc$

Where is mistake?

Algebra IAnswered question

aplaya4lyfeSS1 2022-11-23

Solve the system of equations ${x}^{2}={y}^{3},{x}^{y}={y}^{x}$ in positive real numbers.

Algebra IAnswered question

Jared Lowe 2022-11-20

Consider the following system of linear equations:

${x}_{1}+2{x}_{2}+{x}_{3}-2{x}_{4}=10$

$-{x}_{1}+2{x}_{2}+{x}_{3}-{x}_{4}=6$

$+{x}_{2}+{x}_{3}=2$

Find all its canonical forms and basic solutions.

${x}_{1}+2{x}_{2}+{x}_{3}-2{x}_{4}=10$

$-{x}_{1}+2{x}_{2}+{x}_{3}-{x}_{4}=6$

$+{x}_{2}+{x}_{3}=2$

Find all its canonical forms and basic solutions.

Algebra IAnswered question

Rihanna Bentley 2022-11-19

Solve a system of two equations in which the existence of $ln\left(\frac{\alpha}{\alpha +\beta}\right)$ function makes some limitations in iterations of the Newton-Raphson method.

$\begin{array}{r}\{\begin{array}{l}ln\left(\frac{\alpha}{\alpha +\beta}\right)-{c}_{s1}+\sum _{i\in A}{c}_{i}({\alpha}^{-i}-(\alpha +\beta {)}^{-i})\\ ln\left(\frac{\beta}{\alpha +\beta}\right)-{c}_{s1}+\sum _{i\in A}{c}_{i}({\beta}^{-i}-(\alpha +\beta {)}^{-i})\end{array}\end{array}$

$\begin{array}{r}\{\begin{array}{l}ln\left(\frac{\alpha}{\alpha +\beta}\right)-{c}_{s1}+\sum _{i\in A}{c}_{i}({\alpha}^{-i}-(\alpha +\beta {)}^{-i})\\ ln\left(\frac{\beta}{\alpha +\beta}\right)-{c}_{s1}+\sum _{i\in A}{c}_{i}({\beta}^{-i}-(\alpha +\beta {)}^{-i})\end{array}\end{array}$

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.