Definitions
What is "a set of two or more linear equations that have the same variables"?
System
Where do you plug the estimated ordered pair (x, y) into to see if it is the correct solution after graphing?
Plug the values in for x and y to both equations to see if they work.
Is it possible to check your ordered pair solution to see if its correct after solving by substitution?
Yes, plug in the values for x and y to both equations to see if they work.
What are the two answers that occur with special systems of equations?
No solution and Infinite solutions
Do you get the same solution if you solve a system by graphing as when you solve the system by substitution?
Yes
What is it called when you solve for one variable and plug that equation into the second equation to solve?
Substitution
State what the 2 different methods for graphing a line are.
Table, Intercepts
Explain what would the first 2 things you need to do to solve the system by substitution:
y = -2/3x
y - x = -5
Box in -2/3x and draw an arrow to the y in the second equation.
Substitute -2/3x in for the y to get -2/3x - x = -5
Explain what "infinite solutions" look like by both graphing and by substitution.
Substitution- variables cancel and numbers are the same
Put y + 3x = -2 in function form
y = -3x - 2
Fill in the blank: You would get __________ solution(s) if you solved a system by substitution and got 4 = 4.
infinite
State the 3 steps for solving a system by graphing.
1. Graph both lines on same coordinate plane using one of the 3 methods for graphing
2. Estimate the intersection point
3. Plug in ordered pair for x and y into both equations to see if it works
State the 4 steps for solving a system using substitution.
1. Box in the equation that has either x or y by itself.
2. Plug in expression from box into the correct variable in the second equation to solve for variable
3. Substitute value from step 2 into variable to solve for the second variable
4. Write an ordered pair (x, y)
If you graph the lines y = 6x + 3 and y = 6x - 3, will there be "one solution", "no solution", or "infinite solutions"?
no solution
Both equations in a system have a y-intercept at (0, 2). Is is possible for this system to have infinite solutions? Explain.
Yes, if the lines are both the same
Fill in the blanks: A solution is an ________ ________ that is a solution to ________ equations in the system.
ordered pair; both
Solve the system by graphing:
y = -x + 2
y = 4x + 2
State the solution.
(0, 2)
Solve the system by substitution:
y = 5x
y - 2x = 3
State the solution.
(1, 5)
Solve using either method:
y = 4x - 2
y - 4x = 5
State the solution.
No solution
Solve using either method:
y = 3x
-3x + 5y = 0
State the solution
(0, 0)
Fill in the blanks: ___________ solution(s) exists when the two lines are parallel. ____________ solution(s) exist when the lines are the __________.
No; Infinite; Same
Solve the system by graphing:
y = -x - 1
y = -3x + 9
State the solution.
(5, -6)
Solve using substitution.
x = 3y - 12
2x + 4y = -4
State the solution.
(-6, 2)
Solve using either method:
y = -4/3x + 10/3
4x + 3y = 10
State the solution.
Infinite solutions
Put the equation in function form 3x - 6y = 12
y = 1/2x - 2