May 03, 2015
Equations must be in standard form:
Ax + By = C
Eliminate a variable by using opposites!
May 03, 2015
Warm-Up #5
May 03, 2015
Warm-UP #5
1. Solve the system of linear equations
2. What two methods have we talked about in
solving systems of linear equations?
May 03, 2015
May 03, 2015
May 03, 2015
May 03, 2015
May 03, 2015
May 03, 2015
May 03, 2015
May 03, 2015
Solve the following systems of equations by elimination.
2x + y = 5
x-y=1
Are the equations in
Standard Form?
Are there any opposites?
2x + y = 5
+x- y=1
3x = 6
x=2
Plug "2" into either equation!
2x + y = 5
2(2) + y = 5
4+y=5
y=1
(2, 1)
May 03, 2015
Solve the following systems of equations by elimination.
3x + 2y = 7
5x - 2y = 1
Are the equations in
Standard Form?
Are there any opposites?
3x + 2y = 7
+ 5x - 2y = 1
8x = 8
x=1
Plug "1" into either equation!
3(1) + 2y = 7
3 + 2y = 7
2y = 4
y=2
(1, 2)
May 03, 2015
Solve the following systems of equations by elimination.
6c + 7d = -15
6c - 2d = 12
What can we multiply
by to get opposites?
-1(6c + 7d = -15)
-6c - 7d = 15
-6c - 7d = 15
+ 6c - 2d = 12
-9d = 27
d = -3
Plug "-3" into either equation!
6c + 7(-3) = -15
6c - 21 = -15
6c = 6
c=1
(1, -3)
May 03, 2015
Solve the following systems of equations by elimination.
3n - 2t = 16
-5n - 2t = -8
-3n + 2t = -16
+ -5n - 2t = -8
-8n = -24
n=3
What can we multiply
by to get opposites?
Plug "3" into either equation!
-1(3n - 2t = 16)
-3n + 2t = -16
3(3) - 2t = 16
9 - 2t = 16
-2t = 7
t = -3.5
(3, -3.5)
May 03, 2015
Solve the following systems of equations by elimination.
-14x + 4y = 16
7x - 5y = 1
What can we multiply
by to get opposites?
2(7x - 5y = 1)
14x - 10y = 2
-14x + 4y = 16
+ 14x - 10y = 2
-6y = 18
y = -3
Plug "-3" into either equation!
7x - 5(-3) =1
7x + 15 = 1
7x = -14
x = -2
(-2, -3)
May 03, 2015
Solve the following systems of equations by elimination.
6x + 8y = -30
12x + 2y = -18
What can we multiply
by to get opposites?
-2(6x + 8y = -30)
-12x - 16y = 60
-12x - 16y = 60
+ 12x + 2y = -18
-14y = 42
y = -3
Plug "-3" into either equation!
6x + 8(-3) = -30
6x - 24 = -30
6x = -6
x = -1
(-1, -3)
May 03, 2015
Solve the following systems of equations by elimination.
4x + 3y = -24
5x - 8y = 17
What can we multiply
by to get opposites?
-5(4x + 3y = -24)
-20x - 15y = 120
4 (5x - 8y = 17)
20x - 32y = 68
-20x - 15y = 120
+ 20x - 32y = 68
-47y = 188
y = -4
Plug "-4" into either equation!
4x + 3(-4) = -24
4x - 12 = -24
4x = -12
x = -3
(-3, -4)
May 03, 2015
May 03, 2015
Solve the following systems of equations by elimination.
2x + 3y = -10
6x + 9y = -30
What can we multiply
by to get opposites?
-3(2x + 3y = -10)
-6x - 9y = 30
-6x - 9y = 30
+ 6x + 9y = -30
0=0
Every solution to one equation
will also work for the other one!
infinite solutions
May 03, 2015
Solve the following systems of equations by elimination.
-4x + 2y = 8
8x - 4y = 10
What can we multiply
by to get opposites?
2(-4x + 2y = 8)
-8x + 4y = 16
-8x + 4y = 16
+ 8x - 4y = 10
0 = 26
There are no solutions to one
equation that will also work for
the other one!
no solution
May 03, 2015
Without showing any work, decide whether each
system has infinite solutions or no solution
1) 5x - 2y = 10
5x - 2y = 12
No Solution
3) 2x + 7y = -5
6x + 21y = -15
Infinite Solutions
2) -3x + 5y = 10
12x - 20y = -40
Infinite Solutions
4) 6x - 2y = 3
12x - 4y = -6
No Solution
May 03, 2015
CHALLENGE: - Solve using elimination
3y - 30 = 5x
-2x = 12 + 6y