Tugas Basic Math Soal SPLTV SMA Global Prestasi By: Rachelle Raine

1. R A C H E L L E R A I N E A G N E T H A V O L A R E A N D E R S

3. Ali = 3 buku tulis, 1 pena, 2 pensil = Rp 11.000,00  3x + y + 2z = 11.000 … ( 1 )
Budi = 2 buku tulis, 3 pena, 1 pensil = Rp 14.000,00  2x + 3y + z = 14.000 … ( 2 )
Cici = 1 buku tulis, 2 pena, 3 pensil = Rp 11.000,00  x + 2y + 3z = 11.000 … ( 3 )
“x” stands for
books.
“y” stands
for pens.
“z” stands for
pencil.

4. ①Calculate ( 1 ) and ( 2 )
3x + y + 2z = 11.000 | x2 | 6x + 2y + 4z = 22.000
2x + 3y + z = 14.000 | x3 | 6x + 9y + 3z = 42.000 -
-7y + z = -20.000 … ( 4 )
It depends on us which
variables we want to
get rid of. In this case, I
chose “x” In order to get rid of “x”, we need to
make both statements the same.
That is why it is times by 2 and 3.
This way, we can get rid of “x”
This fourth statement, will help
us in finding either “y” or “z”

5. ②Calculate ( 2 ) and ( 3 )
2x + 3y + z = 14.000 | x1 | 2x + 3y + z = 14.000
x + 2y + 3z = 11.000 | x2 | 2x + 4y + 6z = 22.000 –
-y – 5z = -8.000 … ( 5 )
Since in the first calculation
we chose to get rid of “x”,
we must get rid of “x” as
well in this particular
calculation.
We do the same step like we did
before in the first calculation.
Same as the fourth statement, the
fifth statement will help us in
finding either “y” or “z”

6. ③Calculate ( 4 ) and ( 5 )
-y – 5z = -8.000 | x7 | -7y – 35z = -56.000
-7y + z = -20.000 | x1 | -7y + z = -20.000 –
-36z = -36.000
z = 1.000
After we have used the
first, second, and third
statement, now we can
use the fourth and the fifth
to find either “y” or “z”
It is completely up to us to find “y” or
“z” first, but in this matter I chose to
find “z” first.
Same as before, we times
both statements to get rid
of “y” in order to find the
result of “z”

7. Find the result of y
-7y + z = -20.000
-7y + 1.000 = -20.000
-7y = -20.000 – 1.000
-7y = -21.000
y = 3.000
Since we have found the
result of “z”, we can now
find the result of “y” by
choosing either from the
fourth and fifth
statement.
Since we have found the
result of “z”, we can put it
this way in order to find
“y”

8. Find the result of x
x + 2y + 3z = 11.000
x + 2(3.000) + 3(1.000) = 11.000
x + 6.000 + 3.000 = 11.000
x = 11.000 – 6.000 – 3.000
x = 2.000
After we have found “y” and “z”,
it is now possible for us to find
“x”
To find “x”, we need to
use either the first, the
second, or the third
statement since we have
known both “y” and “z”

9. “Dedi membeli 2 buku tulis, 1 pena, dan 1 pensil.”
Using the statement written above, we can conclude that :
2(2.000) + 3.000 + 1.000 = 8.000
So, Dedi needs to pay for Rp 8.000,00.
Since the amount
of books being
bought by Dedi are
two, so we need to
times 2.
Using the rule before in Step 1 :
x = book
y = pen
z = pencil
It is the same as,
2x + y + z = 8.000
(using variables)