Question

What is the process for doing the method of elimination for math systems?

Answer 1

Elimination is the adding or subtracting of two equations used to solve them.

Explanation:

Elimination is the adding or subtracting of two equations used to solve them.

Say you have this equation.
`\left \{ {{x + y=2} \atop {-x+y=6}} \right.`

Notice that the x in both equations are opposites. After adding together we get.

x + y - x + y = 2 + 6

2y = 8

y = 4

x + 4 = 2

x = - 2

(- 2,4)

Say you decide to subtract the equations.

`\left \{ {{x+y=2} \atop {x+2y=8}} \right.`

x + y - x - 2y = 2 - 8

- y = - 6

y = 6

x + 6 = 2

x = - 4

(- 4, 6)

You can also multiply equations to make it easier to substitute.

`\left \{ {{y+x=4} \atop {-2y+2x=8}} \right.`

`\left \{ {{2y+2x=8} \atop {-2y+2x=8}} \right.`

2y + 2x - 2y + 2x = 8 + 8

4x = 16

x = 4

y + 4 = 4

y = 0

(4, 0)