Substitution Basics
3u + z = 15
u = 4
(4,3)
y = 6x - 11
-2x - 3y = -7
(2,1)
8x + y = -16
-3x + y = -5
(-1,-8)
What do you need in order to solve a system using substitution?
An isolated variable
y = 6x - 11
y = 7
(3,7)
4x + 8y = 20
-4x + 2y = -30
(7,-1)
7x + 2y = 24
8x + 2y = 30
(6,-9)
What do you need in order to solve a system using elimination?
Same or opposite coefficients
4x - 3y = 18
x = 6
(6,2)
-6x + 5y = 1
6x + 4y = -10
(-1,-1)
5x + y = 9
10x - 7y = -18
(1,4)
If you do not have same or opposite coefficients when solving by using elimination, what must you first do?
Multiply
y = 5x - 7
y = 28
(7,28)
-3x - 4y = 2
3x + 3y = -3
(-2,1)
-4x + 9y = 9
x - 3y = -6
(9,5)
Which method should you use to solve the following system?
y=x+2
2x+3y=6
Substitution
-5x + y = -3
x = -5
(-5,-28)
y = -2
4x - 3y = 18
(3,-2)
-6x + 6y = 6
-6x + 3y = -12
(5,6)
-7x + y = -19
-2x + 3y = -19
(2,-5)
What method should you use to solve the following system?
2x+3y=6
x+3y=4
Elimination