Solving by Graphing
Fill in the blank.
CROSS
What does "eliminate" mean?
To get rid of, to destroy, ...
Answers may vary.
What kind of equation do you need in order to solve by substitution?
Either x = or y =
Variables need to be equal to something to start!
What is one reason you would use elimination to solve?
Use elimination when everything is stacked on top of each other, equations are in the SAME FORM
everything is lined up, your x's, your y's, your equal signs, and constants
If you have no solution, what kind of lines do you have?
2 parallel lines
What kind of lines give you one solution?
A) parallel lines
B) skew lines
C) same/one line
B) skew lines
Which variable would be easiest to eliminate in this problem? Why?
3x - 4y = 10
5x + 4y = 20
The y would be easiest to eliminate because the coefficients are opposites.
Solve the following system by substitution. Write your solution as an ordered pair.
x = 4
2x + 3y = 17
(4, 3)
Which method would be best to use for this system? Why?
y = 2x
5x + y = 20
Substitution, because there is a y = (we can replace/substitute easily in the equation)
When you graph, you get one line. What is the solution to the system?
Infinitely many solutions
Infinite solutions
How many solutions do you have if the graph shows 2 parallel lines?
Solve the following system by elimination. Write your solution as an ordered pair.
2x - 3y = 12
4x + 3y = 24
(6, 0)
Solve the following system by substitution. Write your solution as an ordered pair.
y = 3x + 13
4y = 12x + 3
No solution
Which method would be best to use for the following system? Why?
3x + 2y = 6
6x + 2y = 10
Elimination, everything is stacked on top of each other (the x's, y's, equal signs, constants). Also, you have the same coefficients so it will be easy to combine.
When you are solving by elimination and your variables the same coefficient (same number in front), do you add or subtract to combine them?
Subtract
Solve the following system by graphing (use desmos to graph). Write your solution as an ordered pair.
-2x + 10y = -18
0 = -y + 18 - 2x
(9, 0)
Solve the following system by elimination. Write your solution as an ordered pair.
2x - 6y = 12
4x - 12y = 24
Infinite solution
Solve the following system by substitution. Write your solution as an ordered pair.
y = -3x + 4
y = 4x - 10
(2, -2)
Besides choosing substitution because it uses y =, what is the other reason when you should use this method?
When you have a coefficient of 1 for one of your variables in one of the equations
Examples:
x - 2y = 8
5x + y = 10
If you are solving by elimination and the coefficients are not the same/opposite numbers, what must you do first?
Multiply so you can either get your x's or y's the same.
Solve the following system by graphing (use desmos). Write your solution as an ordered pair.
6x - 3y = 3
2x - y = 4
no solution
Solve the following system by elimination. Write your solution as an ordered pair.
3x - 2y = 2
5x - 5y = 10
(-2, -4)
Solve the following system by substitution. Write your solution as an ordered pair.
2x + y = 2
3x + 7y = 14
(0,2)
Which method(s) would be best to solve by? Why? *hint there should be more than one*
y = 3x + 5
y = 2x - 3
Substitution because you have y =
and
Graphing because they are in y = mx + b form
What kind of statement gives you no solution? What kind of statement gives you infinite solutions?
Give an example of each: for example # = # .
No solution = false statement
Example: 4 = 6
Infinite solutions = true statement
Example: 2 = 2
Answers may vary.