6x^2-3xy+7y-23x+26=0

Here are useful ways to handle the equation 6x^2 − 3xy + 7y − 23x + 26 = 0.

1. Solve for y in terms of x

• Group the y-terms: y(−3x + 7) = −6x^2 + 23x − 26
• So y = (6x^2 − 23x + 26) / (3x − 7), with x ≠ 7/3

Equivalently, by division:

• y = 2x − 3 + 5/(3x − 7)

2. A convenient factored form

• (3x − 7)(y − 2x + 3) = 5 This makes the asymptotes clear:
• Vertical asymptote: x = 7/3
• Oblique asymptote: y = 2x − 3

3. Intercepts (quick checks)

• y-intercept (x = 0): y = −26/7
• x-intercepts: discriminant of 6x^2 − 23x + 26 = 0 is 529 − 624 = −95, so no real x-intercepts.

4. If you want integer solutions (x, y) From (3x − 7)(y − 2x + 3) = 5, the integer factors of 5 give candidates:

• 3x − 7 = 5 and y − 2x + 3 = 1 → x = 4, y = 6
• 3x − 7 = −1 and y − 2x + 3 = −5 → x = 2, y = −4 Other factor pairs do not yield integers for x.

If you tell me what you want (solve for y, graphing, integer solutions, etc.), I can tailor further.