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Solve Systems of Equations by Elimination
Contributed by: Miles
(Original author: Jarvie)

Solving Systems 

of Equations

Using ELIMINATION

First, you should make sure that one set of variables
has opposite coefficients.
Solve the system of equations by using elimination.
Fill in each blank, then hit "OK".
{
(-4) + 5y = 1
-2x - 5y = 11
-x + 5y = 1
5y = 
y = 
answer
+
-2x - 5y = 11
-x + 5y = 1
(   ,    )
x = 
= 12
+
Solve the system of equations by using elimination.
{
 -2x + 2y = 8
4x - 2y = 6
Solution:
x = 
x    =  14
(     ,     )
4(      ) – 2y = 6
4x - 2y = 6
  – 2y = 6
–2y = 
y = 
+
Solve the system of equations by using elimination.
-3x + 18y = 15
3x - 4y = -1
y
  = 
=
Solution:
3x – 4(       )= -1
(    ,    )
3x – 4y = -1
3x –         = -1
3x = 
x = 
{
Solve the system of equations by using elimination.
5x + 3y = 9
3x - y = 11
•(                ) 
3(      ) – y = 11
3x – y = 11
5x + 3y = 9
3x - y = 11
- y = 11
y = 
Solution:
{
5x   + 3y =  9
x      y = 
x = 
(     ,     )
  x = 
Sometimes, you must multiply both equations in order to get "opposite variables".
Multiply as indicated:
3(-2x + 7y = -8)
{
2(3x - 2y = 12)
-2x + 7y = -8
3x - 2y =  12
+
First solve for y.  Then solve for x.
-6x + 21y = -24
6x -    4y =  24
the x-coordinate is
the y-coordinate is
y = 
+
{
Solve the system using eliminaton.
6x + 4y = 6
x - 4y = -13
x = 
x = 
Solution:
(    ,    )
6(      ) + 4y = 6
6x + 4y = 6
+ 4y = 6
4y = 
y = 
Solve the system of equations by using elimination.
+
{
-2x - 4y = -12
2x + 3y = 9
Solution:
(    ,    )
Is (5, -2) a solution of the system of equations?
{
3x + 4y = 7
x - 2y = 9
Yes
No
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