If 8ab+7b+3a=c, whats the best way to figure out either a or b

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In summary, to solve for a and b when C is a known number, you can use a matrix or differential equations, but they may not be applicable in this situation. There are infinitely many solutions, so a is chosen as the free variable. Knowing that a and b are integers and there is only one solution for a and b to get c, it may be necessary to find another equation equal to c in order to solve the equation.
  • #1
clearwater304
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C is a known number, therefore I would only need to solve for a or b. Whats the best way to solve this, a few things come to mind, using a matrix or differential equations, but I'm not sure how they are applicable to this situation.
 
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  • #2
There are infinitely many solutions. So you're going to have a free variable. So let a be the free variable, then you can easily solve for b.
 
  • #3
I should have mentioned, a and b are integers, and there is only one solution for a and b to get c. I may be able to find another equation that is equal to c. Would I need this in order to solve the equation?
 

Related to If 8ab+7b+3a=c, whats the best way to figure out either a or b

1. How do I solve for a in the equation 8ab+7b+3a=c?

In order to solve for a, you must first isolate the term that contains a. In this case, that term is 3a. To isolate it, you must subtract 7b from both sides of the equation. This will give you the equation 8ab+3a=c-7b. Then, you can factor out the common factor of a, giving you a(8b+3)=c-7b. Finally, divide both sides by (8b+3) to get the value of a.

2. Can I use substitution to solve for either a or b?

Yes, you can use substitution to solve for either a or b. To solve for a, you can substitute the value of b into the equation, giving you 8a(3)+7(3)+3a=c. Then, you can solve for a using the same method as mentioned above. To solve for b, you can substitute the value of a into the equation, giving you 8b(c-3)+7b+3(c-3)=c. Then, you can solve for b in the same way.

3. Is there a shortcut or formula to solve this type of equation?

There is no specific formula for solving equations of this type, but there are some strategies that can make it easier. For example, factoring out common factors and using substitution can help simplify the equation and make it easier to solve for either a or b.

4. Can I use a graphing calculator to solve this equation?

While a graphing calculator can be helpful for graphing the equation and visualizing the relationship between a and b, it is not the most efficient tool for solving this type of equation. It is better to use algebraic methods to solve for a or b.

5. How do I know if I have the correct solution for a or b?

After solving for a or b, you can plug the value back into the original equation to check if it satisfies the equation. For example, if you solve for a and get the value of a=2, you can plug it into the equation and see if the equation holds true. If the equation is balanced, then you have the correct solution.

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