Solving Systems by Graphing
MANUALLY GRAPH TO SOLVE THE SYSTEM:
y = -5
x = 7
(7,-5)
Solve the following System of Equations using Substitution:
-2x-y=-9
5x-2y=18
(4,1)
Solve the following System of Equations using Elimination:
5x+4y=-30
3x-9y=-18
(-6,0)
y=2x+3
-4x+2y=6
What is All Real Numbers?
A solution exists
MANUALLY GRAPH TO SOLVE THE SYSTEM:
y = x-2
x+y = 10
(6,4)
Solve the following System of Equations using Substitution:
2x+y=20
6x-5y=12
(7,6)
Solve the following System of Equations using Elimination:
2x+8y=6
-5x-20y=-15
infinite number of solutions
x-y=5
y+3=2x
What is One?
Dependent
USE YOUR CALCULATOR TO GRAPH TO SOLVE THE SYSTEM:
3x + 6y - 12 = 0
x + 2y = 8
no solution
Solve the following System of Equations using Substitution:
2x+4y=12
x+y=2
(-2,4)
Solve the following System of Equations using Elimination:
8x+14y=4
-6x-7y=-10
(4,-2)
y=5x-20
20x-4y=80
What is All Real Numbers?
Elimination
Eliminate a variable using addition of equations in a system
USE YOUR CALCULATOR TO GRAPH TO SOLVE THE SYSTEM:
y = -2x + 6
x - 3y = -6
(1.71, 2.57)
Solve the following System of Equations using Substitution:
-3x+3y=4
-x+y=3
no solution
Solve the following System of Equations using Elimination:
-2x-9y=-25
-4x-9y=-23
(-1,3)
y=5x
y=3x+8
What is One?
Substitution
Find y= or x= and plug in to the other equation.
MANUALLY GRAPH TO SOLVE THE SYSTEM:
y=3x-9
x+2y = 10
(4,3)
Solve the following System of Equations using Substitution:
y=5x-7
-3x-2y=-12
(2,3)
Solve the following System of Equations using Elimination:
2m=-4n-4
3m+5n=-3
(4,-3)
y=2x+5
-2x+y=3
What is No Solution?
Define: No Solution and why.
What is parallel lines and no intersection.