Transcript solution of an equation in two variables

Pre-Algebra Ch. 8.2 Linear Equations in Two Variables Page
391
Vocabulary:
Equation in two variables
Solution of an equation in two
variables
Graph of an equation in two
variables
Linear Equation
Function Form
An EQUATION IN TWO VARIABLES is exactly what it
implies: 2x - y = 5
To find the SOLUTION OF AN EQUATION IN TWO
VARIABLES when the equation is in function form, you
simply pick two numbers that make the equation true.
Which of these ordered pairs is a solution to the equation? (1,
-3) or (4, 7) Just plug those numbers into the equation and
see if they make a true statement. 2(1) - (-3) = 5 is a true
statement, but 2(4) - 7 = 5 is NOT a true statement. The
answer is (1, -3)
Your turn: Tell whether the ordered pair is a solution of
+ 2y = -8
1. (0,4)
2. (-2, 1)
3. (4, -12)
4. (10, -19)
3x
You can use a table to help you determine solutions to
equations with two variables.
The number of pages p that Donald has left to write for his 30-page research
paper depends on how many days d he writes 5 pages per day. This situation
can be modeled by the equation p = 30 - 5d
d
p
0
30
1
25
2
20
You simply continue the chart in order to find the solution. How many days will it
take Donald to write his paper?
To graph a linear equation: The ordered pairs for the solution
of y = 2x - 1 are:
(1,1)(2,3)(3,5)(-1, -3)(-2,-5)
The solution is
a LINEAR
EQUATION.
Graph the equation:
(1) y = 2x (2) y = 3x - 4
HOMEWORK: CH. 8.2 Page 394
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Example 4: The solution could also be a horizontal or vertical
line - you just have to make sure you plug in some numbers so
you are sure before you graph:
Name an ordered pair that is a solution for:
(1) x = 1
(2) y = -4
You can say that a line is a function unless it is a VERTICAL
LINE.
An equation is said to be in FUNCTION FORM if it is solving
for y. It will be easier to graph a solution if you put the
problem in function form before graphing!!
Write x + 2y = 6 in function form
ANSWER:
x + 2y = 6
-x + x + 2y = 6 - x
2y = 6 -x
1/2(2/1)y = 6(1/2) - (1/2)x
y = 3 - 1/2(x)
Write the equation x + 3y = 3 in function form, make a table of
solutions, graph the solutions and tell whether the relations is
a function:
2x - 3y = 3
2x-2x - 3y = 3 - 2x
-1/3(-3/1)y = 3(-1/3) - 2x (-1/3)
y = -1 + 2/3(x)
Let x = 0 and y = -1
-1 = -1 + (2/3)0
(0,-1) Find other solutions and then graph
HOMEWORK: CH. 6.2 Page 394
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