Let's solve the given equation [tex]\( xy - 4x - 5y + 20 = 0 \)[/tex].
### Step 1: Rearrange the Equation
First, let's rewrite the equation in a more approachable form. We aim to express [tex]\( y \)[/tex] in terms of [tex]\(x\)[/tex].
[tex]\[ xy - 4x - 5y + 20 = 0 \][/tex]
### Step 2: Group Terms
Group the terms involving [tex]\( y \)[/tex] and the constant terms:
[tex]\[ xy - 5y - 4x + 20 = 0 \][/tex]
### Step 3: Factor the Equation
Let's isolate terms involving [tex]\( y \)[/tex]:
[tex]\[ y(x - 5) = 4x - 20 \][/tex]
### Step 4: Express y in Terms of x
We'll solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{4x - 20}{x - 5} \][/tex]
### Step 5: Simplify the Expression
Now, let's simplify the right-hand side:
[tex]\[ y = \frac{4(x - 5)}{x - 5} \][/tex]
Since [tex]\( x \neq 5 \)[/tex], we can cancel [tex]\( x - 5 \)[/tex] in the numerator and the denominator:
[tex]\[ y = 4 \][/tex]
### Final Solution:
Thus, the value of [tex]\( y \)[/tex] that satisfies the equation [tex]\( xy - 4x - 5y + 20 = 0 \)[/tex] is [tex]\( y = 4 \)[/tex].
So, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[ y = 4 \][/tex]
Thus, the complete solution for the given problem is [tex]\( y = 4 \)[/tex].
