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Systems of Linear Equations
Transcript of 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
add the equations to eliminate x
Plug in the value for y
and solve for x
Your solution is
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