System of Linear Equtions

Solving systems with two variables

1. Graph
- find intersection which is the place both equations share the same x, and y.
x-y-1=0 2x+y=-4
x-1=y -2x-4=y
Graph the above equations, 2nd trace, 5:intersect, enter, enter, enter, then you can get the intersection there.
intersection ( -2, -1 )

2. Elimination
5x+4y=6
-3y-2x=1
step 1 : Rearrange each equation, so variables are in same column.
5x+4y=6
-2x-3y=-1
step 2 : Multiply equations by appropriate value to eliminate one variable.
15x+12y=18
+ -8x-12y=-4
___________
7x+ 0y=14
7x =14
x=2

step 3 : Substitute variable into either of the original equations to solve for second variable.
5(2)+4y=6
4y=6-10
4y=-4
y=-1
solution : ( -1, 2 )

step 4 : Check - use calculator to check the answers.

3. Substitution
4x+y=1
2x-3y=4
step 1 : Solve one of the equations for one variable.
4x+y=1
-4x+1=y
step 2: Substitute this expression into other equation.
2x-3y=4
2x-3y(-4x+1)=4
2x+12-3=4
14x=7
x=1/2
y=-4(1/2)+1
y=-2+1
y=-1
solution (-1, 1/2 )