Substitution and Elimination

HelpinHere · Aug 12, 2009, 04:22 PM

Solve by substitution or elimination.

Substitution:
Solve for any of the variables in any of the equations.
Replace that variable with its value in the unused equation.
Simplify the equation
Solve for the unknowns.

Elimination:
Decide which variable you are going to eliminate.
Use your knowledge of fractions to make the coeffecients for that variable the same number, but opposites. (one +, one -)
Add the two equations. One of the variables should disappear.
Solve for the remaining variable.
Solve for the other variable using either equation.

Examples:
$y=2x+1$
$y=x+2$

Sub:
$y=2x+1$
$y=x+2$

$y-2=x$

$y=2(y-2)+1$
$y=2y-4+1$
$y=2y-3$
$-y=-3$
$y=3$

$3=2x+1$
$2=2x$
$1=x$

Elim:
$y=2x+1$
$y=x+2$

$y=2x+1$
$-2y=-2x-4$

$-y=-3$
$y=3$

$3=x+2$
$1=x$
Now, you just do the same thing, but using your equations.
If you get stuck, post what you have gotten, and I'll help you from there.

(Please, someone correct me if I'm wrong.)

KISS · Aug 12, 2009, 04:42 PM

Elimination:
Reverse eqns

Y=4X+4
Y=2X+3

Substract each term

0Y=2x+1 ------> Go from there

HelpinHere · Aug 12, 2009, 04:46 PM

Quote:

Originally Posted by KeepItSimpleStupid

Elimination:
Reverse eqns
Substract each term
Go from there

Huh? Am I missing something? And... Ooh, I see what you did there...
You did it the EASY way,

usaboy94 · Aug 12, 2009, 04:47 PM

Quote:

Originally Posted by KeepItSimpleStupid

Elimination:
Reverse eqns

Y=4X+4
Y=2X+3

Substract each term

0Y=2x+1 ------> Go from there

Thanks

KISS · Aug 12, 2009, 05:29 PM

Your right, the step that wasn't needed is to multiply one of the Multiply eqns by to make it easy to add or subtract.

Example:

Y=4x+4 (1)
10y=5x+3

Multiply to eqn 1 by 10 or fractions, etc.

10y=40x+40 (1)
10y=5x+3

Now subtract

Eqn #1 is still the same when multiplied by a constant

Substitution and Elimination

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