Kurikulum Merdeka Matematika Kelas 9 Bab 1 Sistem Persamaan Linear Dua Variabel

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Hi everyone, welcome back to the

education portal channel. On this occasion,

we will discuss the

9th grade mathematics material, chapter 1, which is about

linear equations in two

variables. Let's start with

the definition of

SPLDV. SPLDV

is an abbreviation for a system of

linear equations in two variables. Do you still remember

in grade 7 about studying

linear equations in one variable there

is only one variable. Now

we will learn how to

solve a problem that

has two

variables. We start by

solving a system of linear equations in

two

variables. There are four general methods that can be

used to solve a system of

linear equations in two variables. There are

graphical methods, substitution methods,

elimination methods, and combined methods. So that

we can understand further, we will discuss them

one by one.

We will discuss the

graphical method when solving

using the graphical method, of course, later

we will draw a graph

where the intersection point is the answer

to what we are looking for, just like

when in a linear equation in one

variable we have to make the value of x

or y to 0 to make it

easy. So, for example, there is a question: Determine the

solution set of the equation 4x

- 3y = 24 and 2x - y = 10. We can

make a table first for each

equation. So, let's try this first, 4x

- 3y = 24 yes so that you remember again

we make a table like this there is 4x -

3y = 24 then there is x y and X Y whose

x is 0 y will also be

0 like

this Well let's try to solve it first when

x = 0 first we write the formula

4x - 3y = 24 Well then just

replace the x with 0 then 4 0 or 4 *

0 - 3y = 24 4 * 0 yes definitely 0 - 3y = 24

so 0 - 3y = 24 then 0 - 3y

automatically is -3y = 24 what we are looking for

y then it becomes y = 24 / -3 So it is known that

y is

-8 Well then the first x y value

is 0, -8 We enter it into the table so it

becomes like this

continue to the second for the value y = 0

then 4x - 3y = 24 y is now

replaced with 0 then it becomes 4x - 3 0

= 24 so 4x - 0 = 24 automatically 4x =

24 we look for the value of x so it becomes X = 24

/ 4 which is x =

6 now the second value of x y is 6.00

We also enter it into the table so

it becomes K like

this Well if now you can try for the

second equation if you

calculate it correctly the result should be

like this

yes after that you just make

a graph using

Cartesian coordinates until it becomes like

this as you can see there is an

intersection point at 3, -4 so clearly

the value of x = 3 and the value of y = -4 so

the sum of the solutions is

3, -4 then the

substitution method according to its name

substitution means exchanging what is

exchanged is not exchanging change for

candy but exchanging the value of

an

equation the steps are first

determine one of the two

equations after choosing after

choosing we determine

which variable to look for first work until we

find the result of the variable after that

enter the result into the

other equation to find out the

result of the variable being sought after

knowing the result of the variable being sought at

the beginning enter it into the initial equation to

find out the results of the other variables

after that find the

dhp Well, for example, there is an example

Determine the value of x and y from the equation 2x

+ y = 3 and X - 3y = 5 then we will

use the substitution method in

this example the admin chooses X - 3y = 5 to

find out the value of y first we write

first X - 3y = 5 then X we will

look for X here to find out the value of

y so X = 5 +

3y now based on the solution above

we know that the value of x is 5 +

3y we enter x = 5 + 3y into

equation 1 again, namely 2x + y = 3

so 2x + y = 3 here is the initial equation formula

then we replace X it is

replaced with 5 + 3y so 2 5 + 3y y

close brackets + y = 3 now remember in

brackets it means multiplied by S1 2 * 5 also

2 * + 3y So 10 + 6y + y = 3 we

solve first 6y + y becomes 7Y

Becomes 10 + 7Y = 3 here is not finished

because we are looking for y so it becomes 7Y = 3

10 moves to -10 so 7Y = -7

remember what we are looking for is y so y = 7

-7 / 7 automatically y =

-1 from this solution we know the value

of y is

-1 Well finally we know the value

of y Now we find the value of x by

entering it into the initial equation which is

X - 3y = 5 well we rewrite

the equation first X - 3y = 5 then

we enter the value of y so x - 3

-1 = 5 well -3 * -1 becomes +3 so x

+ 3 = 5 remember we are looking for X then +3

must move the side so x = 5 - 3 so

automatically x = 2

we now know the value of X

is 2 then the solution set

is HP =

2-1 remember for the solution set

it is always x

y next the

elimination method this method is different with

substitution that plays exchange

here we are as the name suggests elimination then

we will eliminate or

remove one of the variables

the way is to determine

which variable to eliminate first

from the two equations after that

rewrite both equations but

down then make two lines

beside them a little spaced Determine

how many times so we can

eliminate the value of the variable

we want to find After that we can

reduce or add the

two multiplication results

depending on the value itself

finally found the cellphone Well if we

explain using words like this it's difficult

so let's go straight to

the example for example there is an example question

Determine the value of x and y from the equation 2x

+ y = 5 and x - 2y = 0 here the admin

will determine that eliminate

the variable x first so we

write the two equations namely 2x + y = 5

and x - 2y = 0 then remember to make

two lines beside them but

spaced out so it looks like this well

then because we will eliminate

X then automatically the one above

must be multiplied by 1 the one below is multiplied by 2

so that the x is the same Here If 2x * 1 the

result is 2x y * 1 the result is y and

5 * 1 the result is 5 then the bottom is

also the same x * 2 2x -2y * 2 becomes -4y

and 0 * 2 the result is 0 Well here we

have found the new equation

so that x-n disappears, roughly how should it be

subtracted, so

we make a line like this then

subtract 2x di- x 2x - 2x the result is 0

then y di- di- 4y becomes 5y Why is

this 5y remember negative meets negative

the result becomes positive so y + 4y is

5y 5 - 0 is 5 so from here it is

very easy to find out that y is only 5 / 5

automatically y is

1 now we look for the X value then we

have to eliminate y as usual We

also enter the equation again 2x + y =

5 and x - 2y = 0 we make another line 2

Well now remember we eliminate y

so that the same as the top y

means that the top y must

be 2y so it must automatically be multiplied by 2

while the bottom one is still multiplied by

1 so the result is 2x * 2 the result

is 4x pos Y * 2 so + 2y and 5 *

2 the result is 10 while the bottom one is the same

Now our task is to

eliminate y How do you do it?

Because the top one is positive and the

bottom one is negative, it is impossible for us to

subtract it So the result is just

added so 4x + X the result

is 5x 2y + 2y +

-2y + 2 + -2 the result is 0 so the y is gone

and 10 + 0 is 10 from here it

is known that x = 10 di / 5 so x = 2

Now we know the value of X then the

solution set is HP =

2.1 next is the

combined method from the name alone we can

guess that this method uses a

combination of two methods but the method

Is that a combined method that

combines the elimination and

substitution methods sounds difficult because

There are two methods that must be combined

but it is actually a favorite method

when I was in school or when I was

teaching because the method is easy,

namely using the elimination system

first to determine one

variable and then substituting the

elimination results into another equation. So,

to make it easier, let's give an example of this question.

Determine the value of x and y from the equation

2x + y = 5 and x - 2y = 0. We will

eliminate the variable x so we write

the equation 2x + y = 5 and x - 2y = 0. The

same as before, here's how to make two

more lines. Then we want to eliminate

X, then the one above is multiplied by 1, the one below is

multiplied by 2.

So the result is 2x + y = 5 and

2x - 4y = 0 because we want to eliminate X,

then we just

subtract it so it becomes 5y = 5 y is left 5 / 5

y = 1. We already know that y is =

1. Now we look for the value of x, we

substitute it into the second equation by

entering the value of y, so it becomes x - 2y =

0. So, we have know the value of y earlier,

it becomes x - 2 1 = 0 then X - 2 = 0

we just move the segment so it becomes

x = 2 the result is the same, right? the hp is

2.1 Well, maybe that's enough,

thank you for watching the learning video

until the end, hopefully it will be useful for

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