Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{:[ay=2x+1],[y=2x+2]:}
Consider the system of equations, where
a is a constant. For what value of
a are there no
(x,y) solutions?

$\begin{array}{r} a y=2 x+1 \\ y=2 x+2 \end{array}$ $\newline$ Consider the system of equations, where $a$ is a constant. For what value of $a$ are there no $(x, y)$ solutions?

View step-by-step help

View step-by-step help

Domain and range of absolute value functions: equations

Full solution

Q.

\begin{array}{r} a y=2 x+1 \\ y=2 x+2 \end{array}

\newline

Consider the system of equations, where

a

is a constant. For what value of

a

are there no

(x, y)

solutions?

Identify Inconsistent Condition: The system of equations is given by $ay = 2x + 1$ and $y = 2x + 2$ . To find the value of $a$ for which there are no solutions, we need to look for a condition that would make the system inconsistent. This would occur if the two equations represent parallel lines, which means they have the same slope but different $y$ -intercepts.
Convert Second Equation: The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. The second equation is already in slope-intercept form with a slope of $2$ . To compare it with the first equation, we need to express the first equation in terms of $y$ .
Express First Equation in y: To express the first equation in terms of y, we divide both sides by $a$ to get $y = \frac{2}{a}x + \frac{1}{a}$ .
Set Slopes Equal: Now we have $y = \frac{2}{a}x + \frac{1}{a}$ and $y = 2x + 2$ . For the lines to be parallel, the slopes must be equal, which means $\frac{2}{a}$ must be equal to $2$ . Setting these equal gives us $\frac{2}{a} = 2$ .
Solve for $a$ : Solving for $a$ , we multiply both sides by $a$ to get $2 = 2a$ . Then we divide both sides by $2$ to get $a = 1$ .
Analyze Solutions: When $a = 1$ , the two equations have same slopes and different $y$ -intercepts, which means the system has no solution. $\newline$ Therefore, for $a = 1$ there are no solutions for the given system of equations.

More problems from Domain and range of absolute value functions: equations

Question

What is the domain of this function?

\newline

(9,–2)(6,–10)(–3,9)(5,2)

\newline

\newline

(A)\{–3,5,6,9\}\newline(B)\{–10,–2,2,9\}\newline(C)\{2,5,6,9\}\newline(D)\{–6,–3,5,9\}

Posted 1 month ago

Question

Look at this set of ordered pairs:

\newline

(2, 14)

\newline

(10, 12)

\newline

(3, -19)

\newline

Is this relation a function?

\newline

\newline

\text{[[yes]}

\text{[no]]}

Posted 1 month ago

Question

Use the following function rule to find

f(11)

\newline

f(x) = -10 - 7x

\newline

f(11) =

Posted 1 month ago

Question

Find the slope of the line

y = -3x - \frac{2}{5}

\newline

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

\newline

\_\_\_\_\_

Posted 1 month ago

Question

A line has a slope of

3

and passes through the point

(-2,-10)

. Write its equation in slope-intercept form.

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

Posted 1 month ago

Question

What is the range of this function?

\newline

\newline

\newline

\text{all real numbers}

\newline

\{y \mid y \geq 0\}

\newline

\{y \mid y \leq 0\}

\newline

\{y \mid y > 0\}

Posted 2 months ago

Question

g(x)

g(x)

is the translation

1

f(x) = |x|

\newline

Write your answer in the form

a|x - h| + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

What is the domain of this function?

\newline

(8,–1)(7,–11)(–4,10)(4,3)

\newline

\newline

(A)\{–4,4,7,8\}\newline

(B)\{–11,–1,3,10\}\newline

(C)\{3,4,7,8\}\newline

(D)\{–7,–4,4,8\}

Posted 3 months ago

Question

What is the domain of this function?

\newline

(10,\,–3)(2,\,–9)(–5,\,8)(3,\,1)

\newline

\newline

[\{–5,2,3,10\}][\{–9,\,–3,1,8\}][\{1,2,3,10\}][\{–10,\,–5,2,3\}]

Posted 1 month ago

Question

What is the domain of this function?

\newline

(1,–4)(9,–12)(–6,11)(7,5)

\newline

\newline\\(A)\{–6,1,7,9\}\newline

(B)\{–12,–4,5,11\}\newline

(C\{5,1,7,9\}\newline

(D)\{–9,–6,1,7\}

Posted 1 month ago