Find all solutions to:

ab + 2a + 2b = −16

ac + 2a + 2c = 26

bc + 2b + 2c = −14.

juananother Feb 22, 2021

#1**+2 **

Find all solutions to:

ab + 2a + 2b = −16

ac + 2a + 2c = 26

bc + 2b + 2c = −14

**Hello juananother!**

\( ab + 2a + 2b = −16\\ a(b+2)+2b=-16\\ a= -\dfrac{16+2b}{b+2}\\ \ \\ ac + 2a + 2c = 26\\ a(c+2)+2c=26\\ a= \dfrac{26-2c}{c+2} \)

\( -\dfrac{16+2b}{b+2}=\dfrac{26-2{ \color{BrickRed} c}}{{ \color{BrickRed} c}+2} \)

\(bc + 2b + 2c = −14\\ \color{BrickRed} c=( -\dfrac{14+2b}{b+2}) \)

\(-\dfrac{16+2b}{b+2}= \dfrac{26-2{ \color{BrickRed} (-\dfrac{14+2b)}{b+2}}}{{ \color{BrickRed} (-\dfrac{14+2b}{b+2})}+2}\)

\(b= -\dfrac{8}{3}\)

\(c= -\dfrac{14+2\cdot (-\dfrac{8}{3})}{-\dfrac{8}{3}+2}\)

\(c=-13\)

\(a= \dfrac{26-2(-13)}{(-13)+2} \)

\(a=-\dfrac{52}{11}\)

!

asinus Feb 22, 2021

#2**+1 **

There have been at least two other (with better methods than this one) answers to this question posted within the last week.

Look for them.

Guest Feb 22, 2021

#3**+1 **

"with better methods than this one" Is there any better math than right? At school?

!

asinus
Feb 22, 2021

#4**0 **

Some methods are certainly better than others.

(Both good and bad methods should lead to the correct answer.)

Have you looked at the earlier answers ?

Guest Feb 22, 2021