Question

Please Help!! - Find constants a and b so that (8, −7) is the solution of the system. Please answer in exact numbers.

Answer 1

Explanation:

Plug in 8 for x, and -7 for y in both systems.

`8a- 7b = 10`

`8b - 7a = - 5`

Now, we use the elimination method to isolate a or b.

Let multiply the top equation by 8 and the bottom one by 7.

`64a - 56b= 80`

`56b - 49a = - 35`

Eliminate the b variable by adding the two systems.

`15 a= 45`

`a = 3`

Now, plug 3 for a into either the systems to find b.

`24 - 7b = 10`

`- 7b = - 14`

`b = 2`