Graphing
Answer must be drawn on a graph:
y= x+1 y= -x +1
(0,1)
y = 6x − 11
−2x − 3y = −7
(2, 1)
−4x − 2y = −12
4x + 8y = −24
(6,-6)
What are the 3 steps for graphing?
1) ALL equations in slope intercept
2) Graph both lines
3) Answer (x,y) where lines cross
"Putting all equations in slope intercept form"
Step #1
Answer must be drawn on a graph:
y= x+4 y= x-4
No solution
2x − 3y = −1
y = x − 1
(4, 3)
4x + 8y = 20
−4x + 2y = −30
(7, −1)
What are the 6 steps for Substitution?
1. Slope intercept form
2. Plug in equation
3. Solve for x
4. plug x in to og. equation
5. Solve for y
6. Answer (x,y)
Which method does not require putting both lines in slope intercept form?
Elimination
Answer must be drawn on a graph:
y= 2x+2 y= -x -4
(-2,-2)
y = −3x + 5
5x − 4y = −3
(1, 2)
−6x + 5y = 1
6x + 4y = −10
(−1, −1)
What are the 6 steps for elimination?
1. Identify opposites
2. Subtract Down
3. Solve for x or y
4. Plug into OG equation
5. Solve for y or x
6. Answer (x,y)
Which method would you use for: 2x+3y=6 x-3y=7
Answer must be drawn on a graph:
y= -2x+2
2x+y=-2
No Solution
−3x − 3y = 3
y = −5x − 17
(−4, 3)
−6x + 6y = 6
−6x + 3y = −12
(5, 6)
What method is this?
y=-1
y=2x+3
-1=2x+3
-4=2x
-2=x
y=2(-2)+3
y=-4+3
y=-1
(-2,-1)
Substitution
Which method would you use to solve: 4x+3y=9 -x+7y=4
Substitution
Answer must be drawn on a graph:
y=1/2x +3 -x+2y=6
Infinite Solutions (Same Line)
y = −2
4x − 3y = 18
(3, −2)
−4x + 9y = 9
x − 3y = −6
(9, 5)
What method is this? Is the answer correct?
2x+3y=3
3x-3y=0
-x=3
x=-3
2(-3)+3y=3
-6+3y=3
3y=9
y=3
(-3,3)
Elimination and yes
The answer to all systems of equations problems is written as ___.
(x,y) or a coordinate point where he lines cross