By Graphing
What do you need to identify from each equation before solving by graphing?
The slope (m) and the y-intercept (b).
Solve:
y = 2x + 5
y = 3x + 5
(0, 5)
Solve:
x + y = -5
x - y = 5
(0, -5)
-2x + 3y = 6
2x -3y = 6
0 = 12
No solution
How many types of solutions exist for a system of equations? Name them.
3
One Solution, Infinitely Many Solutions, No Solution
What is the slope and y intercept in each of the following equations?
y=3x+2
y=-1/2x-7
M=3 b=2, M=-1/2 b=-7
Solve:
x=2y-4
x=-8y+16
(2, 0)
Solve:
2x - 5y = 10
4x - 10y = 20
Infinitely Many Solutions
Solve:
7x - 3y = 21
-7x + 3y = -21
0 = 0
Infinitely Many Solutions
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)
Solve:
y=x+3
y=2x+5
(-2,1)
Solve:
3x-y=-2
-2x+y=3
(1,5)
What is the solution? Pick a method and solve.
-x +y =5
x -5y=-9
(-4, -1)
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)
Solve:
x=2y-4
x+8y=16
(0,2)
Solve:
x +2y = 5
3x+2y = 17
(6, -1/2)
What is the solution? Pick a method and solve.
y=x+5
4x+y=20
(3, 8)
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)
Solve:
x=y-8
-x-y=0
(-4,4)
Solve:
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.