How do you solve 8a+2b=11 and 5a-6b=25?

1 Answer
May 23, 2018

Answer:

#a=2, b=-5/2#

Explanation:

We have the following system:

#8a+2b=11#

#5a-6b=25#

We want to eliminate one of the variables so we can solve for the other. So let's multiply the first system by #3#. We get

#24a+6b=33#

#5a-6b=25#

Now we can add both systems to get

#29a=58#

Dividing both sides by #29#, we get

#color(blue)(a=2)#

We've solved for one of the variables, now we can plug into an equation to solve for the other.

I'll plug into the first equation. We get

#8(2)+2b=11#

which simplifies to

#16+2b=11#

#=>2b=-5#

#=>color(blue)(b=-5/2)#

Now, we've solved for both of our variables.

Hope this helps!