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 ______?
intersect
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
What is an arithmetic sequence?
list of numbers that go up/down by the same amount each time
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?
isolate for one of the variables in one of the equations
What is the last step when solving a system by elimination?
sub your variable into either of the original equations and solve for the remaining variable
What is the common difference?
the difference between terms in an arithmetic sequence
Which method tends to be the most error-prone?
Graphing
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)
When would solving by elimination be easier than solving by substitution?
when the x's or y's are already identical and can be eliminated right away
An arithmetic sequence has a first term of 10 and a common difference of 3. What is the 12th term?
t12 = 10+(12-1)(3)
t12 = 10+(11)(3)
t12 = 10+33
t12 = 43
Which method would be easiest to solve this system of equations?
y=-2x+3
y=4
What does a system of linear equations with infinite solutions look like on a graph?
Solve this system of equations by substitution:
y=x-2
y=-2/3x+3
(3, 1)
Solve the system of equations using elimination:
3x-6y=3
4x+6y=32
(5, 2)
An arithmetic sequence has a first term of 10 and a common difference of 3. What term number has a value of 67?
67 = 10+(n-1)3
67 = 10+3n-3
67=7+3n
60=3n
20=n
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)
30=a+9d
54=a+21d
-24=-12d
d=2
30=a+9(2)
30=a+18
a=12