Solving a System by Graphing
Which equations would you use graphing to find the solution?
a. y=2x+8 and y=3x-4
b. 2x+3y=12 and -2x+4y=20
c. 4x+2y=12 and y=2x+3
A
When solving a system by graphing, both equations should be in slope intercept form (y=mx+b).
Which equations would you use substitution to find the solution?
a. y=2x+8 and y=3x-4
b. 2x+3y=12 and -2x+4y=20
c. 4x+2y=12 and y=2x+3
C.
It is best to use substitution when you are given a value for a variable. (In this case, you are told what y equals.)
Which equations would you use elimination to find the solution?
a. y=2x+8 and y=3x-4
b. 2x+3y=12 and -2x+4y=20
c. 4x+2y=12 and y=2x+3
B.
When using elimination, both equations are set up with the form Ax+By=C. In this example, -2x and 2x are opposites and will ELIMINATE one another.
If x=2, what is the solution to: 3x+5?
11.
If x=2, you write "2" in place of the "x". Then, you solve.
How do you write the solution to a system?
a. As an ordered pair (x,y)
b. As an ordered pair (y,x)
a. As an ordered pair (x,y)
An ordered pair (the pair of numbers you are graphing) is ALWAYS in the order (x,y).
**HACK: x comes first in the alphabet, so x is first in the ordered pair!
Mr. T has already solved a problem using substitution. He found that x=2 and y=-4. He writes that the answer is: (-4, 2). What did Mr. T do INCORRECTLY?
He wrote the solution in the wrong order! THIS MAKES THE ENTIRE ANSWER INCORRECT.
X is always first in an ordered pair. The correct answer for x=2 and y=-4 is written: (2, -4).
How do you eliminate a term? What term would be eliminated in the example?
Hint/example:
2x+3y=16
-2x+4y=20
Terms are eliminated by being exact opposite (2x and -2x).
Solve for p in the following equation.
p+20=40
20.
You do the inverse (subtract 20 from both sides).
Which term best describes the two lines represented by the equations below?
𝑦=3𝑥 − 5
𝑦=3𝑥 - 5
a. the same line
b. parallel
c. intersecting
a. The same line
The slope (3) and the y-intercept (-5) are the same, so the line is exactly the same! If you graphed this, you would be drawing one line on top of the other because they are THE SAME.
If you are given the following system, what is the first step to substitute?
2x+3y=12
y=3
Put the 3 in place of the y.
The equation would change from
2x+3y=12
to
2x+3(3)=12
-3x+2y=15
3x+4y=15
Eliminate a term.
Solve for y.
The terms that eliminate each other are -3x and 3x because they are opposites.
y=5
Solve for y in the following equation:
2y=18
y=9
The inverse operation is to divide both sides by 2.
When given the equation y=3x+12, what is first point that you graph? Which number? And WHY?
12.
12 would be the first point graphed on the y-axis (up and down, vertical). It is the y-intercept.
With the following system, what would the equation look like after you substituted?
y=4
2x-3y=12
2x-3(4)=12
The 4 was put in place of y because y represents 4.
When you eliminate a term, how do you combine the other terms?
Example:
2x+3y=20
-2x+4y=29
You add the other terms.
3y+4y=7y
20+29=49
The new equation is: 7y=49
Solve for x in the following equation:
2x+10=30
x=10
To get x by itself, you must do the inverse operation.
First, subtract 10 from both sides.
Then, divide both sides by 2.
X is now by itself! :)
You have graphed two lines as part of the system. Where do you find the solution?
The solution is where the two lines intersect (cross). This is an ordered pair.
After you solve for the first variable, what is your next step?
Plug that variable in to solve for the other variable.
Work together as a team. How far can you get with solving by elimination?
-2x+4y=10
2x+3y=11
x=1
y=3
This should be written as an ordered pair: (1 ,3)
Solve for r in the following equation:
2(3r+4)=32
r=4
First, distribute the 2 to each term inside of the parantheses.
Then, solve for r by using inverse operations.