By Graphing
What do you need to identify from each equation before solving by graphing?
What the slope is (m) and what the y-intercept is (b).
Which equation will I use to substitute and where should I put it?
3x + 2y = 8
y = -4x
y = -4x and put the (-4x) into 3x + 2(-4x) = 8 and solve for x.
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.
How many equations are in a system of equations?
2 or more
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
How do use substitution to solve?
x=2y-4
x=-8y+16
Set them equal to each other and solve for y.
2y-4 = -8y + 16
How can you eliminate a variable that has opposite coefficients?
Add the opposite coefficients.
What is one reason that you would choose to solve by substitution?
Both equations are solved for a variable or 1 equation is solved for a variable.
What should your answer be written as when solving systems?
An ordered pair.
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
How do you check your answer when solving systems of equations?
You plug the ordered pair back into both equations and see if you get the same number on both sides of the equals sign for both equations.
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.