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Systems of Equations -Elimination
Contributed by: Gibson
(Original author: Jarvie)
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 + 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
?
Have a good day!
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