Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

4y-3x=40

4y=3x-30
Which of the following accurately describes all solutions to the system of equations shown?
Choose 1 answer:
A
x=0 and
y=0
(B)
x=(5)/(3) and
y=(45)/(4)
(c) There are infinite solutions to the system.
(D) There are no solutions to the system.

$4 y-3 x=40$ $\newline$ $4 y=3 x-30$ $\newline$ Which of the following accurately describes all solutions to the system of equations shown? $\newline$ Choose $1$ answer: $\newline$ (A) $x=0$ and $y=0$ $\newline$ (B) $x=\frac{5}{3}$ and $y=\frac{45}{4}$ $\newline$ (C) There are infinite solutions to the system. $\newline$ D There are no solutions to the system.

View step-by-step help

View step-by-step help

Solve rational equations

Full solution

Q.

4 y-3 x=40

\newline

4 y=3 x-30

\newline

Which of the following accurately describes all solutions to the system of equations shown?

\newline

Choose

1

answer:

\newline

(A)

x=0

and

y=0

\newline

(B)

x=\frac{5}{3}

and

y=\frac{45}{4}

\newline

(C) There are infinite solutions to the system.

\newline

D There are no solutions to the system.

Analyze the equations: Analyze the given system of equations. $\newline$ We have two equations: $\newline$ $1$ . $4y - 3x = 40$ $\newline$ $2$ . $4y = 3x - 30$ $\newline$ We need to determine the relationship between these two equations to find the solution set.
Compare the equations: Compare the two equations. $\newline$ By looking at the two equations, we can see that they are not identical. To better understand their relationship, we should try to express both equations in terms of one variable, for example, $y$ .
Express first equation in terms of y: Express the first equation in terms of y. $\newline$ From the first equation, we can solve for y: $\newline$ $4y - 3x = 40$ $\newline$ $4y = 3x + 40$ $\newline$ $y = \frac{3x + 40}{4}$
Express second equation in terms of y: Express the second equation in terms of y. $\newline$ The second equation is already solved for y: $\newline$ $4y = 3x - 30$ $\newline$ $y = \frac{3x - 30}{4}$
Compare expressions for $y$ : Compare the expressions for $y$ from both equations. $\newline$ We have: $\newline$ From equation $1$ : $y = \frac{3x + 40}{4}$ $\newline$ From equation $2$ : $y = \frac{3x - 30}{4}$ $\newline$ These two expressions cannot be equal for any value of $x$ because they differ by a constant term ( $40$ vs. $-30$ ). Therefore, there is no value of $x$ that will satisfy both equations simultaneously.
Conclude the number of solutions: Conclude the number of solutions. $\newline$ Since there is no value of $x$ that satisfies both equations, the system of equations has no solutions.

More problems from Solve rational equations

Question

Evaluate the expression for

t = -4.4

\newline

Write your answer in simplest form.

\newline

` frac{t - 4}{t - 2} =` ____

Posted 1 month ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{g}{3g^2 - 4g}

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\frac{3}{2} - \frac{5p^3}{3}

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{1 + \frac{v^5w}{3}}{1}

\newline

Posted 2 months ago

Question

h

\newline

\frac{-5}{h - 2} = \frac{-4}{h - 3}

\newline

1

2

\newline

h =

h =

Posted 1 month ago

Question

What is the equation of the vertical asymptote of

y = \frac{1}{x + 9}

Posted 2 months ago

Question

What is the excluded value for

y = \frac{1}{x - 9} - 9

\newline

Posted 2 months ago

Question

Simplify. Write your answer using whole numbers and variables.

\newline

\frac{9k + 4}{9k^2 + 4k}

\newline

Posted 2 months ago

Question

Divide. Write your answer in simplest form.

\newline

\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)

\newline

Posted 2 months ago

Question

Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{5 - \frac{3}{t^3}}{1}

\newline

Posted 2 months ago