General
Name the three methods used for solving linear systems.
Graphing, Substitution, Elimination
y = x + 1
y = 2x + 1
x = 0, y = 1
x + y = 7
2x + y = 10
x = 3, y = 4
x + y = 12
x - y = 0
x = 6, y = 6
y = 2x + 1
y = -3x + 1
Graphing
What is the first step of substitution?
Pick one equation and solve for one variable.
y = 2/3x - 1
y = -3x - 1
x = 0, y = -1
−5x + y = −2
−3x + 6y = −12
x = 0, y = -2
x + 3y = 1
−3x − 3y = −15
x = 7, y = -2
a + b = 10
a - b = 2
Elimination
When using the elimination method, what do you do if no variables are eliminated when the equations are combined?
Use multiplication on one equation
y = -2/3x + 2
y = 2/3x - 2
x = 3, y = 0
−5x + y = −3
3x − 8y = 24
x = 0, y = -3
-4x + y = 6
-5x - y = 21
x = -3, y = -6
x + 2y = 5
2x + 3y = 8
Substitution
When using the graphing method to solve linear systems, how do you know where the solution is?
The solution is the point where the two lines intersect.
y - x = 1
y + 2x = 4
x = 1, y = 2
2x + y = 20
6x − 5y = 12
x = 7, y = 6
−3x − 4y = 2
3x + 3y = −3
x = -2, y = 1
10x + 3y = 13
-10x + 4y = -6
Elimination