Substitution help

Feb 2010
3
0
How to do these problems:

Substitution
Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution of Infinitely many solutions

1. 2x + 5y= 38
x - 3y = -3

2. x - 4y = 27
3x + y = -23

3. 2x + 2y = 7
x - 2y = -1

4. 2.5 + y = -2
3x + 2y = 0

PLEASE HELP ME!!! I've BEEN TRYING TO DO THIS SINCE 5:00 and its 10:39!!!!! YOU DESERVE A COOKIE IF YOU ARE ABLE TO HELP ME!!!!
 
Nov 2009
517
130
Big Red, NY
How to do these problems:

Substitution
Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution of Infinitely many solutions

1. 2x + 5y= 38
x - 3y = -3
\(\displaystyle 2x + 5y= 38\to (1)\)
\(\displaystyle x - 3y = -3 \to (2)\)

\(\displaystyle (2)\implies x = -3+3y\)

Now, sub this \(\displaystyle x\) into \(\displaystyle (1)\)

\(\displaystyle 2\left\{-3+3y\right\} + 5y= 38\)

\(\displaystyle \implies -6 + 11y = 38 \implies \fbox{y = 4}\)

Now, sub this back into either \(\displaystyle (1)\) or \(\displaystyle (2)\) to find out what \(\displaystyle x\) is.

You try some...