###
**Substitution**

Very similar to the method of substitution for systems of linear equations- Solve for one variable in one of the equations
- Substitute the value of that variable in another equation
- Solve for variable in that equation
- Solve for other variables using known variable value
- Double check to make sure the ordered pairs work by plugging them back into an equation

### Elimination

Also very similar to the method of substitution for systems of linear equations- Multiply by a constant
- Add/subtract to get rid of a variable
- Solve for the variable
- Solve for other variables using known variable value
- Double check to make sure the ordered pairs work by plugging them back into an equation

Here’s an example using substitution (click here):

1. Solve for y in the second equation

2. Substitute x+1 for y in the first equation

3. Solve for x

4. Solve for y by substituting in the values for x

5. Double check

Here’s an example using elimination (click here):

1. We don’t need to multiply by a constant because already has the same constant of 1 in both equations.

2. Subtract to get rid of

3. Solve for y

4. Solve for x

5. Double check

Last example (click here):

You have to do a lot of algebraic manipulation when solving systems of equations, especially with nonlinear equations. Practice an array of different types of systems of nonlinear equations to become very familiar with solving these problems.

Until next time,

Leah

To minimize, you can use a generalized algorithm that matches the matrix. Such a way of solving a multidimensional problem will be further described as a multidimensional generalized global search algorithm.

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