By Graphing
How many steps are there total to solve systems by substitution?
3
When is the elimination method convenient for solving a system of equations?
When there are equal or opposite coefficients for one of the variables.
When is graphing the best method for solving a system of equations?
When both equations are in slope intercept form or can easily be turned into slope intercept form.
What is m and b in each of the following equations?
y=3x+2
y=-1/2x-7
M=3 b=2 M=-1/2 b=-7
Do we have to complete step 1 if the system is as follows?
x=2y-4
x=-8y+16
No, 1 or more equations are solved for a variable.
How can you eliminate a variable that has opposite coefficients?
Add the opposite coefficients.
What is the solution to the following system of equations? (You have to graph them)
y=x-3
y=-x-1
(1,-2)
What is the solution to the following system?
y=x+3
y=2x+5
(-2,1)
Solve:
3x-y=-2
-2x+y=3
(1,5)
What method would you use if you had the following system of equations?
-x+y=5
X-5y=-9
Elimination
What is the solution to the following system of equations? (You have to graph them)
y=-2x-1
y=x+5
(-2,3)
What is the solution to the following system?
x=2y-4
x+8y=16
(0,2)
Solve:
x +2y = 5
3x+2y = 17
(6, -1/2)
What method would you use if you had the following system of equations?
y=x+5
4x+y=20
Substitution
It is possible to have no solution to a system of linear equations. When solving by graphing what would this look like?
Two lines that are parallel and do not intersect.
What is the solution to the following system of equations? (You have to graph them)
y=-x+6
y=x
(3,3)
What is the solution to the following system?
x=y-8
-x-y=0
(-4,4)
What is the solution to the following system?
x-y=-3
5x+3y=1
(-1,2)
What is the solution? Pick a method and solve.
y=x+5
y=2x
(5,10)
It is possible to have infinitely many solutions to a system of linear equations? When solving by graphing what would that look like? What would the equations look like?
Yes. The same line. They would have the same slope and y-intercept.