Download Linear Equations in Two Variables

LINEAR EQUATIONS IN TWO
VARIABLES
June 26, 2012
LINEAR EQUATIONS IN TWO VARIABLES
2x + 3y = 6
y = 4x – 5
Note: In linear equation in two variables,
 The exponent of each variable must be 1
 The two variables cannot be part of the term
 And no variable can appear in the denominator
of a fraction
STATE WHETHER OR NOT THE EQUATION IS
A LINEAR EQUATION IN TWO VARIABLES
1. 10x = 2y – 5
Linear Equation in Two
Variables
____________________
Not a Linear Equation in
Two Variables
2. x2 + y2 = 1
____________________
3. 4xy + 2y =8
Not a Linear Equation in
Two Variables
____________________
x
y

 12
4.
2
6
5. 6x – 4y + 3z = 12
Linear Equation in Two
Variables
____________________
Not a Linear Equation in
Two Variables
____________________
EQUATION OF A LINE
The most fundamental type of equation in two variables
is a linear equation. A linear equation in two variables is
an equation that can be written in the form.
Ax + By = C
This form of a linear equation in two variables is said to be
in standard form.
A standard graphing form of a linear equation in two
variables is an equation that can be written in the form.
y = mx + b
This form of a linear equation in two variables is said to be
in y-form (slope-intercept form).
EQUATION OF A LINE


Write each equation in standard form
1. 6x = 2y – 12
2. 6 = 7x – 2y
3. 4x + 3 = 3y + 5
4. 7x – 2y + 14 = 0
Write each equation in the y-form
1. x + 4y = 12
2. 3y = 6x + 2
3. 2x – 5y = 15
4. 3x = 8y
THE SUM OF TWO NUMBERS, X AND Y, IS 8
x+y=8
Based on the equation:
If x = 2,
y= 6
Can yyou
give other
x = 3,
= 5
of this
x = – 1 solutions
y= 9
x=–2
yequation.
= 10
The ordered
pairs
(2,6), (3,5),
(-1,9), (-2,10)
are some of
How
many
solutions
does
the solution of the equation x + y = 8.
the
equation
have?
Thus, a solution of a linear equation in two variables is
an _______________
that satisfies the equation.
ordered pair
Determine whether the pairs ( -2 , -10 ), ( 0 , 2 ) and ( 1 , 2 )
are solutions of the equation y = 4x – 2

Solution: To determine whether each pair is a solution, we
replace x by first coordinate and y by second coordinate.
When the replacements make the equation true, we say
that the ordered pair is a solution.
y = 4x – 2
?
–10 = 4(–2) – 2
?
y = 4x – 2
?
2 = 4(0) – 2
?
y = 4x – 2
?
2 = 4(1) – 2
?
–10 = –8 – 2
2=–2
2=4–2
–10 = –10 true
2 = –2 false
2 = 2 true
DETERMINE WHETHER OR NOT THE GIVEN ORDERED
PAIR IS A SOLUTION OF THE GIVEN EQUATION.
1. 3x + 4y = 32
(4 , 5)
Solution
____________________
2. y = 5x + 3
(-2 , 13)
Not a Solution
____________________
(6 , 7)
Solution
____________________
(3 , 4)
Not a Solution
____________________
(1, – 1)
Not a Solution
____________________
3. 2x = y + 5
4.
x
y

9
2
3
5. 7x – 2y = 5
COMPLETE THE ORDERED PAIRS FOR EACH
EQUATION
1. 5x + y = 12 (0 , __) ; (2 , __) ; (__ , 27)
2. x + y = 5
(__ , 5) ; (5 , __) ; (__ , -2)
3. x = 3y + 20 (5 , __) ; (__ , -2) ; (__ , 6)
4. y = –3x
(2, __) ; (-2, __) ; (3, __)
5. x = 2y – 1
(__ , 3) ; (__ , ½) ; (__ , 0)
GRAPHING LINEAR EQUATIONS BY
POINT-PLOTTING
The basic method of graphing an equation is by pointplotting. The idea is to plot as many points that satisfy
the equation, until a clear picture of the graph is drawn
 To graph the linear equations in two variables we follow
the following steps:

Change the equation into standard graphing form y = mx + b
where m and b are real numbers
 Make a table of values at least three (assign a real number to
x the independent variable then solve for the corresponding
value of y the dependent variable)
 Plot the points on the Cartesian plane
 Draw a line connecting the point, then label it with the
equation.

COMPLETE THE TABLE THEN DRAW THE
GRAPH
1. y = 3x – 5
x 0 2 3
y -5 1 4
.
.
.
COMPLETE THE TABLE THEN DRAW THE
GRAPH
1. y = –4x + 2
x 1 2 0
y -2 -6 2
.
.
.
COMPLETE THE TABLE THEN DRAW THE
GRAPH
1. x – 3y = 7
x -2 1 4
y -3 -2 -1
.
.
.