Methods
What are the three methods for solving systems of equations?
Graphing, substitution, elimination
When graphing a system of equations, the solution lies where the lines ______?
intersection/cross
What is an advantage of solving by substitution instead of graphing?
more exact answers, less errors, faster, easier
What is the first step when solving a system by elimination?
rearrange so the equations are lined up the same way
x + 6 + 2x = 9
x = 1
Which method would be easiest to solve this system of linear equations?
4x-3y=-2
2x-3y=6
Elimination
What does a system of linear equations with no solution look like on a graph?
parallel lines
What is the first step of solving a system by substitution?
plug in one of the variables into the other equation
What is the last step when solving a system by elimination?
plug your variable into either of the original equations and solve for the remaining variable
52 - 5n = 2
n = 10
If you graph the two lines, this is the place where you find the solution to the system of equations.
The intersection
What do linear equations share if their system has "no solution"?
same slope
Solve this system of equations using substitution:
y=-3
y=6x+3
(-1,-3)
Solve this system of equations by elimination
x - y = 1
x + y = -9
(-4,5)
3m + 3 = 4m + 1
m = 2
Which method would be easiest to solve this system of equations?
y=-2x+3
y=4
Substitution
What does a system of linear equations with infinite solutions look like on a graph?
identical lines, overlapping at every point
Solve this system of equations by substitution:
y=3x-2
y=-2x+8
(2, 4)
Solve the system of equations using elimination:
3x-6y=3
-4x-6y=-32
(5, 2)
2(2b + 6) - 6 = 38
b = 8
True or false: you will get a different answer if you solve a system with graphing vs. elimination.
False - you should get the same answer
Can a system of linear equations have two solutions? Explain your answer clearly.
No - can't intersect twice!
Solve this system of equations by substitution:
y=-3x
-3x+3y=0
(0, 0)
Solve the system of equations using elimination:
2x+8y=-22
x+5y=-12
(-7, -1)
2y + 22 + 3y = 2(3y + 5)
y = 12