Solving Systems of Equations, algebra homework help

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Solving Systems of Equations, algebra homework help

When you are solving a system of equations algebraically you have three options.

One: the equations meet at one point and that one point is your solution.
Two: the equations are parallel and never intersect. You have no solution.
Three: the equations are the same and thus you have infinite solutions.

Elimination Method

For elimination you are trying to eliminate one of the variables. So for example if you have, 2x+y=8 and 3x-2y=6 write them one below the other like so:

2x+y=8

3x-2y=6

I need one of the variables to be eliminated. I am going to choose “y”. So I am going to multiply the first equation by 2 to get : 2(2x+y =8) –> 4x+2y = 16

I then write them below each other again:

4x+2y = 16

+3x-2y=6 and add them together to get (notice the y’s cancel or are eliminated):

——————–

7x = 22

I can then solve for x to get x = 22/7

To solve for “y” plug in my answer for “x” into either original equation.

Now try and solve:
3x + 2y = 4
-2x – y = 8