Solving a system by substitution

Question

5a+7b=-21

a+18=-6b

 

 

I have a problem when you have to move the equation and make it into one. 

Answer 1

1. 5a+7b=-21
2. a+18=-6b

 

We can easily isolate a in the second equation by subtracting 18 from both sides. The equation then becomes a=-6b-18. We can then substitute the right side of the equation in for a in the first equation. That then becomes 5(-6b-18)+7b=-21. We then distribute the 5 to get -30b-90+7b=-21. Combining the b terms gives us -23b-90=-21. Adding 90 to both sides gives us -23b=69. Divide both sides by -23 means b=-3.

 

Now we substitute -3 for b in one of the original equations. 5a+7(-3)=-21. Multiply and get 5a-21=-21. Adding 21 to both sides yields 5a=0. Divide both sides by 5 and you have a=0.