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Systems of Equations Elimination
Contributed by: Jarvie

Solving

Systems of Equation

Using

ELIMINATION

a
b
c
d
e
Solving Systems by Using Elimination!
Put the steps in the correct order!
Then add the two equations together.
One of the variables should be eliminated!

Write the ordered pair!  It's your ANSWER!
Take that answer and plug it back intoone of the original equations to find the other variable.
Solve for the first variable.
Make sure one of the sets of variables has opposite coefficients.You may have to multiply one or both equations by a number to make this happen.
e, a, c, d, e
d, a, e, c, b
d, c, a, e, b
e, c, a, d, b
First, make sure that one set of variables has
opposite coefficients.
Fill in all the blanks, then press "ok"
{
(-4) + 5y = 1
-2x - 5y = 11
-x + 5y = 1
y = 
answer
+
-2x - 5y = 11
-x + 5y = 1
(   ,    )
x = 
= 12
Solve
{
 -2x + 2y = 8
4x - 2y = 6
Answer
(     ,     )
Sometimes, you will have to multiply one of 
the equations by a number to get one set 
of "opposite variables."
{
What should you multiply the second equationby to make the x variable "opposite variables?"
3x - 4y = -1
x - 6y = -5
-6
3
-3
-4
After multiplying the second equation by -3, 
what does the second equation look like?
{
3x - 4y = -1
x - 6y = -5
-3x - 18y = -5
-3x + 18y = -5
-3x + 18y = 15
-3x - 18y = 15
Solve this system.
{
3x - 4y = -1
x - 6y = -5
(     ,     )
{
Solve.
3x - y = 11
5x + 3y = 9
(     ,     )
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
+
Solve for y.  
-6x + 21y = -24
6x -    4y =  24
the x-coordinate is
the y-coordinate is
Then solve for x.
{
-3x + 5y = -16
Solve.
-5x - 4y = -2
(     ,     )
Solve.
{
-6x + y = 11
2x + 3y = 13
(     ,     )
{
Solve.
6x + 4y = 6
x - 4y = -13
(     ,     )
Solve.
{
-2x - 4y = -12
2x + 3y = 9
(     ,     )
Solve.
{
(     ,     )
2x - y = 6
x + 4y = 12
Is (5, -2) a solution of
{
3x + 4y = 7
x - 2y = 9
Yes
No
?
Is (-1, 3) a solution of
Yes
No
{
-4x + 3y = 13
15x + 3y = -6
?
Jeff sells a total of 30 adult and children's tickets for $102. If children's tickets cost $2.50 and adult tickets cost $4,how many of each ticket did he sell?
# of children's tickets 
# of adult tickets
Have a good day!
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