How do you know what to substitute in Solving Systems by Substitution?
y=3x+2
7x-4y=7
how and why would you substitute?

Question

How do you know what to substitute in Solving Systems by Substitution?
y=3x+2
7x-4y=7
how and why would you substitute?

anonymous · Answer

If you have a single variable in any equation, you can find an actual value for that variable. Substituting in a small equation into another equation is a method to find a value.

So you've got this equation: y=3x+2. We know that's what y equals. All we have to do is take a look at the second equation and think about our next step. Well...We could just drag the little equation, y=3x+2, into 7x-4y=7, and see what we get! 

7x - 4(3x+2) = 7   ...When (3x+2)=y

See what happened? When I substituted in y=3x+2, I ended up with an equation with one single variable: X.  

Now, just solve! 

7x - 12x - 8 = 7    - We used distribution here.
-5x - 8 = 7            - Got rid of two like-terms.
-5x = 15                - Added .-8 and 7
x = -3!                   - We found a value!!!!

Now, use this information to find y!

y = 3x + 2
y = 3(-3) + 2
y = -7

And we've got our answers.

^_^

anonymous · Answer

Always substitute the simplest looking equation into another given equation. I picked y=3x+2 instead of 7x-4y=7 because I knew right off the bat would y equaled.