Systems of equations :$

*Systems of equations is asked when there are two equations. One must use both to find a coordinate; x and y.
*This is called solving linear systems algebraically.


Solve the system of equations 2x - 3y = 23  +3y=23and -x- 6y= -4 
by combining the equations.

1) First eliminate x.

2x - 3y = 23   -x - 6y = -4

Use both 2 and -1, to eliminate x.

1(2x - 3y = 23)   2( -x - 6y = -4)    Distribute.

2x - 3y = 23

-2x - 12y = -8           2)Make sure to eliminate x, one is positive and one is negative.

____________

0x - 15y = 15

     _________

       -15    -15

y = -1                3) Now use y to find x. Plug in -1 to an easy equation.

2x - 3(-1) = 23

2x + 3 = 23

     -3      -3

__________               

2x = 20

______

    2

x = 10

(10,-1)

Done!