#### Transcript of Systems of Linear Equations

**Systems of Linear Equations**

What is a System of Linear Equations?

It is a grouping of two or more linear equations in the same variables.

Solving a System by Graphing

Write each equation in slope-intercept form: y = mx + b

Draw the line for each equation

Find the point of intersection by identifying the coordinates (x,y) that lie on both lines

Check that your answer is valid for both equations.

Solving a System with Elimination

Line up your variables

Create opposites with a chosen variable by multiplying one or both of the equations by a number.

Add the equations together to eliminate a variable.

Solve for the remaining variable and plug your answer into one of the original equations to solve for the other variable.

A solution to a system is a coordinate point (x, y) that satisfies both equations. On a graph it is represented by the intersection of the two lines

All you do is SOLVE!

Solving Systems with Substitution

Solve for one of the variables in one of the equations

Replace that variable in the second equation with the equivalent expression found in step 1.

Solve for the remaining variable

When do I use Each Method?

Both Equations are already in slope-intercept form

This also works well with substitution

Set the two equations equal

to each other and solve for x

Plug your answer into one of the original equations

So your solution is

Graph each line and look for the point of intersection

When the terms are aligned, elimination is your best bet

Multiply the second equation by 4 to make the x's opposites

Option 1:

add the equations to eliminate x

Plug in the value for y

and solve for x

Your solution is

Option 2:

Multiply the second equation by 3 to make the y's opposites

add the equations to eliminate y

plug in the value for x and solve for y

your solution is

When one variable has been solved

Replace y with x - 1

Solve for x

Plug in x to find y

Your solution is

Original System

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