Methods & Solutions
Graphing
Substitution
Elimination
Definitions
100
What are the three practiced methods used for solving systems of equations?
"the Graphing Method, the Substitution Method, and the Elimination Method"
100
When graphing a system of equations, the solution lies at the point of ______________?
"intersection"
100
You solved a system of equation using substitution and you ended up with
5=-7
How many solutions does the system have?
No solution
100
What is the first thing you need to check when solving a system by elimination?
The two equations need to have the variables aligned.
100
The answer of a systems of linear equations.
the solution
200
Is the ordered pair (- 2, 8) a solution of
8x + 2y = 0
x - 2y = -18
YES
200
What is the solution of this systems of equations?
(2,2)
200
You solved a system of equation using substitution and you ended up with
0=0
How many solutions does the system have?
infinitely many solutions
200
You solved a system of equations by elimination and ended up with
0=-9
How many solutions does the system have?
No solution
200
Same slope and different y-intercept. The number of solutions for this type of systems of equations is:
none
300
In what method would you replace a variable with something of equal value?
Substitution
300
What do the linear equations, in a system, share if their point of intersection is "no solution"?
What is "the same slope"?
300
The solution of the following system of equations:
y=-3
y=6x+3
(-1,-3)
300
The solution of the following system of equations using elimination.
3x-6y=3
4x+6y=32
(5,2)
300
The format used to write a solution of a system of linear equations.
an ordered pair
(x,y)
400
Which method would you use to solve this system of linear equations?
y=-2x+3
y=4
"the Substitution Method"
400
What does a system of linear equations, with infinitely many solutions, look like when graphed?
the same line multiple times
400
Solve the following system of equations using substitution.
y=x+6
x+2y=6
(3, 1)
400
The solution of the following system of equations using elimination:
-5x - 5y = -15
x + 8y = -4
(4,-1)
400
Same slope and y-intercept. What is the number of solutions for this type of system of equations?
infinitely many
500
Is the ordered pair (-1,2) a solution of x-y=-3 and 2x+y=0?
YES
500
NO SOLUTION
500
The solution of the following system of equations:
y=-3x
-3x+3y=0
What is "(0, 0)"?
Show your work to your teacher.
500
The solution of the following system of equations:
2x+8y=-22
x+5y=-12
(-7, -1)
500
Adding an inverse is the same as _____________.
subtraction