What are the three ways to solve a linear system?
elimination
graphing
substitution
Solve Using Graphing:
y = -3
y = 5/3x + 2

When using substitution, what is the first step?
To isolate a variable.
What is the first step when using elimination?
Equations must be lined up in the same order.
when graphing linear inequalities what type of line does < and > use?
Dotted Line
When should I use substitution?
When it is easy to solve for x or y. (isolate a variable)
Solve the systems of linear equations by graphing:


Solve the systems of equations using substitution
x=-3
x - 3y=-15
(-3,4)
Use ELIMINATION to solve each system of equations.
-3x + 2y = 23
-5x - 2y = 17
(-5, 4)
What type of line does ≤ and ≥ get when graphing linear inequalities
solid line
When should I use elimination?
After equations are lined up, it is "easy" to make opposite coefficients.
What is the solution?

(-1,1)
Solve the systems of equations using substitution:
y = 6x
2x + 3y=-20
(-1,-6)
Use ELIMINATION to solve each system of equations.
-4x + 7y =-13
4x - 7y =3
no solution
How is graphing systems of inequalities different than graphing systems of equations?
they use dotted lines sometimes and you have to shade to find the solution
What is the last step when solving by substitution or elimination?
Substitution
How many solutions are there?

No Solutions
Solve the systems of equations using substitution:
x - 4y=0
x+2y=12
(8,2)
Use ELIMINATION to solve each system of equations.
2x+ 3y = 5
-8x - 12y = -20
infinite solutions
Systems of inequalities can only be solved by ______
graphing
When using the substitution method, what would be the first step when solving for x in the first equation?
5x +5y = 10
8x + 4y = 0
Subtract the 5y
How many solutions are there?

Infinitely Many Solutions
Use substitution to solve the following system of equations.
2x + y = 3
8x + 4y =12
infinitely many solutions
Use ELIMINATION to solve each system of equations.
x + y = 4
2x - 5y = 15
(5,-1)
Solve the system:
y ≤ x − 2
y > −3x + 5
