Question

-x+1/4y+5/4=0;x=5
Answer should be y=4x-5, y= 15

Make sure it variable before constant
Improper fractions (no mixed fractions or decimals)
Variable at the top
Only 1 Sign
Write in proper descending order

So far I started off by the common denominator so -x+1/4y+5/4=0;x=5
Common denominator of 1/4 and 5/4 is 4 so
1/4 times 4/1 = 4/4 = 1 and 5/4 times 4/1 = 20/4=5
So our problem now is -x+1y+5=0 is that right? Athena after I’m supposed to solve in descending order or undoing the problem like PEMDAS but the opposite so SADMEP but I kinda lost can you help please

Answer 1

You're on the right track with rewriting your equation! Let's take it step by step to help you transform the equation and find the correct form for \( y \).

Starting with your equation:

\[
-x + \frac{1}{4}y + \frac{5}{4} = 0
\]

To eliminate the fractions, the common denominator for the terms with the fractions is 4. Multiply the entire equation by 4:

\[
4(-x) + 4\left(\frac{1}{4}y\right) + 4\left(\frac{5}{4}\right) = 0
\]

This simplifies to:

\[
-4x + 1y + 5 = 0
\]

Now, we can write it in a clearer form:

\[
-y + 4x + 5 = 0
\]

To make it look like \( Ax + By + C = 0 \) and isolate \( y \), let's rearrange the equation to get \( y \) on one side. Move \( 4x \) and \( 5 \) to the right:

\[
y = 4x + 5
\]

So, we indeed have:

\[
y = 4x + 5
\]

Next, since you want \( y \) in terms of \( x \) and you mentioned \( x = 5 \), let's substitute \( x \) with \( 5 \):

\[
y = 4(5) + 5
\]

Calculating gives:

\[
y = 20 + 5 = 25
\]

It looks like there was a misunderstanding with the \( y \) value you might have provided (15 does not match 25 as per the substitution).

However, if you want your final equation in the specified format with \( Ax + By + C = 0 \) and only one sign you can rearrange it like this:

Starting from:

\[
y - 4x - 5 = 0
\]

To maintain the form you indicated would prefer to be:

\[
4x - y + 5 = 0
\]

This is still equivalent but emphasizes \( Ax + By + C = 0 \) where \( A = 4 \), \( B = -1 \), and \( C = 5 \). Let me know if you have further questions or need more explanation on any step!