# Substitution and Elimination

Y=2X+3
Y=4X+4 Solve by substitution or elimination. I need step by step.

 HelpinHere Posts: 1,062, Reputation: 747 Ultra Member #2 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 Posts: 12,602, Reputation: 4378 Uber Member #3 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 Posts: 1,062, Reputation: 747 Ultra Member #4 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 Posts: 18, Reputation: 1 New Member #5 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 Posts: 12,602, Reputation: 4378 Uber Member #6 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

## Check out some similar questions!

Elimination or substitution [ 5 Answers ]

I have tried to see both ways of eliminationa and substitution and I am having a hard time with this problem. I have the answer, I want to see how to GET the answer. I need to see work and steps please, and thank you. By the way, the answer is (4,2) 7x-2y=24 5x+4y=28

Algebra substitution and elimination [ 7 Answers ]

Ok so I need help with my homework I don't get how to do it :( 4x+3y=1 X=1-y So far I have 4(1-y)+3y=1 4-4y+3y=1 -1/-1 =1/-1

Elimination or substitution Equation [ 3 Answers ]

Solve the following system by substitution or elimination 2x-4y=3 -3x+6y=7

Elimination or Substitution and how do I do it? [ 1 Answers ]

^=exponent Y^2=25 X^2-2x=4x+16 :eek:

Substitution or Elimination [ 1 Answers ]

Y=-2x-3 4x+3y=3 Someone help me with my homework!