All about Systems of Equations
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution
Special Cases
Grab Bag
100
What is slope-intercept form?
y=mx+b
100
How many possible solutions can a system of linear equations have?
one, none/zero, or infinitely many solutions (the line itself)
100
If you were to use substitution method and your friend uses graphing method on the same system of equations would both get the same solution?
Yes.
Every equation graphs a specific line so no matter how you solve, you get the same solution!
100
Solve the system:
2x+y=9
-2x-y=-9
These are the same line, so all points on the line are solutions
or
{ (x,y) | 2x+y=9 }
100
What are the three practiced methods used for solving systems of equations?
What are "the Graphing Method, the Substitution Method, and the Elimination Method"?
200
True or False:
It does not matter which method you use when solving systems of linear equations because they will all give you the same answer.
True
200
How many solutions will a set of parallel lines have?
Zero
200
What is the first step when solving a system of linear equations using the SUBSTITUTION method?
Isolate one of the variables in one of the equations
then
substitute into the other equation
200
Solve the system:
y=2x+4
y=2x+5
No solution because they are parallel lines (same slope)
200
What do the linear equations, in a system, share if their point of intersection is "no solution"?
What is "the same slope"?
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point (x, y) where the 2 lines intersect.
300
How many solutions will the system in the graph have?
1 solution
300
Solve the system:
y=2x
3x+y=20
3x+(2x)=20 or
5x=20
x=4
y=8
(4,8)
300
Solve the system:
y+3x=7
y=-3x+7
They are the same line, so all points on the line are solutions
or
{ (x,y) | y = -3x+7}
300
The solution of the following system of equations:
y=−3y=-3
y=6x+3
What is "(-1,-3)"?
400
At least how many linear equations will be in a system of linear equations?
At least 2 linear equations
400
What is the solution to the system of linear equations?
(2,2)
400
How would you isolate x in this equation?
6y+x=20
Subtract 6y from both sides to get:
x=20-6y
400
Solve the system:
9x+3y=7
9x+3y=5
No solution, they are parallel lines.
400
Same slope and y-intercept. What is the number of solutions for this type of system of equations?
What is "infinitely many"?
500
How do we write solutions to systems of linear equations?
(x, y)
500
What is the solution to the system of linear equations?
{ (x,y) | y=2x+1}
or all points on the line
500
Use the substitution method to solve the system of linear equations:
x=3y
x+y=20
(3y) + y = 20
4y=20
y=5
x=15
(15,5)
500
Solve the system:
y-2x=4
y-4=2x
They are the same line so there are infinitely many solutions, all the points on the line
or
{ (x,y) | y = 2x+4 }
500
The solution of the following system of equations:
2x+8y=−222x+8y=-22
x+5y=−12
What is "(-7, -1)"?