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).
What is the first step to solving systems of equations by substitution?
Solve one equation for one variable.
What is the first step to solve systems of equations by elimination?
What should both of your equations look like when you choose to solve by graphing? What format should they be in?
y=mx+b Slope intercept form Both solved for y
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
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 already.
What do you need one of your variables to have so you can eliminate with addition? What do they look like?
Opposite coefficients. Same number in front of x or y terms with one positive and one negative.
What is one reason that you would choose to solve by substitution?
Both equations are solved for a variable. 1 equation is solved for a variable. A variable in either equation has a coefficient of 1 or -1.
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 because the x variable already has matching coefficients with one positive and one negative.
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, because one equation is already solved for one variable.
It is possible to have no solution to a system of linear equations. When solving by graphing what you that 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.