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The general form of SLETV We have to learn about

Solving the SLETV Solving the word problems

The general form of SLETV

A system of linear equations in two variable Contains in two or more linear equations in two variable ax + by = p cx + dy = q

a) 3x + y = 6 X+y=4

With a, b, c, d, p, and q are real number

b) 3x + 4y = 18 5X + 2y = 16

Solving the SLETV

Graph method Subtitutiom method Elimination method

Mixed method

How to solve with graph method

1. Determine the intersection point of each linear equations in two variables. The intersection point with x axis y=0 and the intersection point with y axis x=0 2. Determine the intersection point in the cartesian coordinate then connect them in a line

3. The intersection line in the cartesian coordinate will appear the intersection point of two linear equations in two variable. This intersection point is the solution of the SLETV

Y

7

6 5 4 ( 1, 3)

3X + Y = 6

3

2

X+Y=4

1 0

1

2

3

4

5

6

7

8

x

How to solve with subtitution method

1.

Consider the equation of ax +by = p. If p ≠ 0, then expres y in x and you will get y =

2.

p q

+

a b

x

Subtitute y in the second equation and you will get LEOV in the form of cx + d (

p

+ q

a b

x) = q

3. Solve this linear equation in one variable to get the value of x 4. Subtitution the value of x into the equation of ax + by + p to get the value of y

3x + 4y = 18 5x + 2y = 16

How to solve with elimination method 1. Eliminate variable of x ax + by = p x c cx + dy = q x a

acx + bcy = acx + ady = aq ( bc – ad ) y = - aq

y=

– aq bc - ad

2. Eliminate variable of y ax + by = p x d cx + dy = q x b

adx + bdy = dp bcx + bdy = bq ( ad – bc ) x = dp - bq

7x - y = 2 x + 3y = 16

x=

dp – bq ad - bc

How to solve with mixed method This method is combining elimination and subtitution methods 1. Eliminate variable of x ax + by = p cx + dy = q

xc xa

acx + bcy = acx + ady = aq ( bc – ad ) y = - aq

y=

– aq bc - ad

2. subtitute variable of y into second equation to get the value of x cx + d ( y =

– aq bc - ad

)=q

3x + 2y = 23 x - 6y = 11

Solving the word problems 1. Three years ago, the sum of dad’s age and mom’s age was 58 years. In the next five years, the sum of dad’s age plus twice of mom’s age will be 110 years. How old are dad and mom at the present? Word problems

Change into

Evaluate the result

Result

resulting

Mathematical expressions (SLETV) Solved by

Graph method Subtitutiom method Elimination method Mixed method