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The line ax+(a+1)y=a+2 passes through the point (4,-8). Find a.

 Mar 3, 2020
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ax + (a + 1)y  =  a + 2

 

We are given that  (4, -8)  is a solution to this equation.

That means if we substitute  4  in for  x  and  -8  in for  y ,  we will make a true equation.

So the following equation must be true:

 

a(4) + (a + 1)(-8)  =  a + 2

                                            We can distribute  -8  to the terms in parenthesees and simplify the left side of the equation.

4a - 8a - 8  =  a + 2

                                            Add  8  to both sides of the equation.

4a - 8a  =  a + 2 + 8

                                            Subtract  a  from both sides of the equation.

4a - 8a - a  =   2 + 8

                                            Combine like terms.

-5a  =  10

                                            Divide both sides of the equation by  -5

a  =  -2

 

Check: https://www.desmos.com/calculator/cq30o2b4j7

 Mar 3, 2020

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