Graphing
y = 2x + 2
y = x - 1
(-3, -4)
y = 2
3x + 2y = 10
(2, 2)
x + 3y = 5
2x -3y = -8
(-1, 2)
This consists of two or more linear equations in the same variables.
What is a system of linear equations? (linear system)
This is the sum of 7 and 3
(5 x 2)
y = 2x + 4
y = 3x + 2
(2, 8)
x + 3y = 2
-x + 2y = 3
(-1, 1)
-5y + 8x = -18
5y + 2x = 58
(4, 10)
The solution to a system of inequalities is called this.
What is the feasible region?
The method of solving equations where you add or subtract equations to end up with one variable.
Elimination
What is the solution to the system x = 10, y=10?
(x, x)
x = 3
y = 2x + 1
(3, 7)
x - 2y = -10
3x - y = 0
(2, 6)
3y - 5x = -26
-2y - 5x = -16
(4, -2)
You could try this to describe where to shade when graphing an inequality.
What is test a point to see if it makes the inequality true or false?
How can you tell if a linear system has infinitely many solutions?
The equations are the same or solving the system provides a true statement with no variables.
This is the product of 55 and 2
100+5+5
4x + 2y = 8
2x + y = 4
No solution
2x – 3y = –2
4x + y = 24
(5, 4)
3x−4y=8
18x−5y=10
(0, -2)
y≤x−2
y>−3x+5
(Shaded toward the bottom right)
A linear system will have this if the lines are parallel with different y-intercepts.
What is no solution?
Wimbeldon and The French Open are championships associated wtih this sport
(5+5)nis
y = 1/2 x + 2
y = 1/4 x + 4
(8, 6)
5x - y = -13
-5x +2y = 24
no solution
4x−9y−2=0
12x−5y+38=0
(-4, -2)
2x – 3y < 12
x + 5y < 20
Darkly shaded top left corner
You need at least this many equations to solve a problem that uses 4 variables.
What are 4 equations?
This is the solution to the system x + y = 9 and x - y = 9
What is (0, 9)