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

Answer 1

To solve the equation \(-x + \frac{1}{4}y + \frac{5}{4} = 0\) for \(y\) and express it in the desired format, let’s follow these steps:

1. First, isolate \(y\):
\[
\frac{1}{4}y = x - \frac{5}{4}
\]

2. Multiply both sides by 4 to eliminate the fraction:
\[
y = 4x - 5
\]

Now, you mentioned setting \(x = 5\) to find the corresponding value of \(y\):

3. Substitute \(x = 5\) into \(y = 4x - 5\):
\[
y = 4(5) - 5 = 20 - 5 = 15
\]

So, the equations obtained are:
\[
y = 4x - 5, \quad y = 15
\]

These satisfy your requirements:
- The variable \(y\) is on the left, before the constant.
- There are no mixed fractions or decimals.
- Each equation is expressed in proper descending order.

Answer 2

For how we are doing it in my class we first clear off the fractions in our equation by multiplying by our common denominator so what I have is 4 as the common denominator of 1/4 and 5/4 is that right?

Answer 3

Yes, you are correct! The common denominator for the fractions \( \frac{1}{4} \) and \( \frac{5}{4} \) is indeed \( 4 \).

To clear the fractions from the equation \(-x + \frac{1}{4}y + \frac{5}{4} = 0\), you can multiply the entire equation by \( 4 \) to eliminate the fractions:

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

This simplifies to:

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

Now, isolate \(y\):

\[
y = 4x - 5
\]

This is the same result as before, and it keeps the variable before the constant. Now you can substitute \( x = 5 \):

\[
y = 4(5) - 5 = 20 - 5 = 15
\]

So to summarize:
- The cleared equation is: \(-4x + y + 5 = 0\) or, rearranged, \(y = 4x - 5\).
- When \(x = 5\), you find \(y = 15\).

Your understanding of clearing fractions with a common denominator is spot on!