1. Linear Equations in Two Variables
June 26, 2012

2. 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

3. State whether or not the equation is a linear equation in two variables
1. 10x = 2y – 5 ____________________
2. x2 + y2 = 1 ____________________
3. 4xy + 2y =8 ____________________
____________________
5. 6x – 4y + 3z = 12 ____________________
Not a Linear Equation in Two Variables
Not a Linear Equation in Two Variables
Linear Equation in Two Variables
Not a Linear Equation in Two Variables

4. 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
in y-form (slope-intercept form).

5. 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

6. The sum of two numbers, x and y, is 8
x + y = 8
Based on the equation:
If x = 2, y =
x = 3, y =
x = – 1 y =
x = – 2 y =
The ordered pairs (2,6), (3,5), (-1,9), (-2,10) are some of
the solution of the equation x + y = 8.
Thus, a solution of a linear equation in two variables is
an _______________ that satisfies the equation.
Can you give other solutions of this equation.
How many solutions does the equation have? 6 5 9 10
ordered pair

7. 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
–10 = –8 – 2
–10 = –10 true
y = 4x – 2
2 = 4(0) – 2
2 = – 2
2 = –2 false
y = 4x – 2
2 = 4(1) – 2
2 = 4 – 2
2 = 2 true ? ? ? ? ? ?

8. Determine whether or not the given ordered pair is a solution of the given equation.
1. 3x + 4y = 32 (4 , 5) ____________________
2. y = 5x + 3 (-2 , 13) ____________________
3. 2x = y + 5 (6 , 7) ____________________
4. (3 , 4) ____________________
5. 7x – 2y = 5 (1, – 1) ____________________
Not a Solution
Solution
Not a Solution
Not a Solution

9. 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)

10. Graphing linear equations by point-plotting
The basic method of graphing an equation is by point- plotting. 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.

11. Complete the table then draw the graph
1. y = 3x – 5 . x 3 y 1 2 . -5 4 .

12. Complete the table then draw the graph
1. y = –4x + 2 x 1 y -6 2 . -2 2 . .

13. Complete the table then draw the graph
1. x – 3y = 7 x -2 4 y 1 -3 -1 . . .