Math worksheet with a riddle involving solving systems of equations using the addition method.

Let's solve each system of equations using the multiplication method with the addition (elimination) method, as instructed. We’ll find the solution for each system, match it to the corresponding word in the answer column, and then decode the joke.

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🔍 Step-by-step solutions:

We are given 12 systems labeled A–L. For each, we'll solve using elimination (multiply equations so that one variable cancels out).

---

#### A)
$$
\begin{align*}
5x - 2y &= 4 \quad \text{(1)}\\
3x + y &= 9 \quad \text{(2)}
\end{align*}
$$

Multiply equation (2) by 2:
$$
6x + 2y = 18
$$

Add to (1):
$$
(5x - 2y) + (6x + 2y) = 4 + 18 \Rightarrow 11x = 22 \Rightarrow x = 2
$$

Plug into (2):
$$
3(2) + y = 9 \Rightarrow 6 + y = 9 \Rightarrow y = 3
$$

✔ Solution: $ (2, 3) $

→ Matches BIRDSEED → Letter: B

---

#### B)
$$
\begin{align*}
3x - 5y &= 13 \quad \text{(1)}\\
x - 2y &= 5 \quad \text{(2)}
\end{align*}
$$

Multiply (2) by 3:
$$
3x - 6y = 15
$$

Subtract (1):
$$
(3x - 6y) - (3x - 5y) = 15 - 13 \Rightarrow -y = 2 \Rightarrow y = -2
$$

Plug into (2):
$$
x - 2(-2) = 5 \Rightarrow x + 4 = 5 \Rightarrow x = 1
$$

✔ Solution: $ (1, -2) $

→ Matches SINGING → Letter: S

---

#### C)
$$
\begin{align*}
7x + 2y &= -1 \quad \text{(1)}\\
3x - 4y &= 19 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 2:
$$
14x + 4y = -2
$$

Add to (2):
$$
(14x + 4y) + (3x - 4y) = -2 + 19 \Rightarrow 17x = 17 \Rightarrow x = 1
$$

Plug into (1):
$$
7(1) + 2y = -1 \Rightarrow 7 + 2y = -1 \Rightarrow 2y = -8 \Rightarrow y = -4
$$

✔ Solution: $ (1, -4) $

→ Matches WHO → Letter: W

---

#### D)
$$
\begin{align*}
x + 2y &= 6 \quad \text{(1)}\\
5x + 3y &= 2 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 5:
$$
5x + 10y = 30
$$

Subtract (2):
$$
(5x + 10y) - (5x + 3y) = 30 - 2 \Rightarrow 7y = 28 \Rightarrow y = 4
$$

Plug into (1):
$$
x + 2(4) = 6 \Rightarrow x + 8 = 6 \Rightarrow x = -2
$$

✔ Solution: $ (-2, 4) $

→ Matches MOO → Letter: M

---

#### E)
$$
\begin{align*}
2x + 3y &= 7 \quad \text{(1)}\\
3x + 4y &= 10 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 3:
$$
6x + 9y = 21
$$

Multiply (2) by 2:
$$
6x + 8y = 20
$$

Subtract:
$$
(6x + 9y) - (6x + 8y) = 21 - 20 \Rightarrow y = 1
$$

Plug into (1):
$$
2x + 3(1) = 7 \Rightarrow 2x = 4 \Rightarrow x = 2
$$

✔ Solution: $ (2, 1) $

→ Matches TWEET → Letter: T

---

#### F)
$$
\begin{align*}
7x - 3y &= -5 \quad \text{(1)}\\
3x + 2y &= 11 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 2:
$$
14x - 6y = -10
$$

Multiply (2) by 3:
$$
9x + 6y = 33
$$

Add:
$$
(14x - 6y) + (9x + 6y) = -10 + 33 \Rightarrow 23x = 23 \Rightarrow x = 1
$$

Plug into (2):
$$
3(1) + 2y = 11 \Rightarrow 3 + 2y = 11 \Rightarrow 2y = 8 \Rightarrow y = 4
$$

✔ Solution: $ (1, 4) $

→ Matches FARMER → Letter: F

---

#### G)
$$
\begin{align*}
3x - 5y &= 7 \quad \text{(1)}\\
5x - 2y &= -1 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 2:
$$
6x - 10y = 14
$$

Multiply (2) by 5:
$$
25x - 10y = -5
$$

Subtract:
$$
(25x - 10y) - (6x - 10y) = -5 - 14 \Rightarrow 19x = -19 \Rightarrow x = -1
$$

Plug into (1):
$$
3(-1) - 5y = 7 \Rightarrow -3 - 5y = 7 \Rightarrow -5y = 10 \Rightarrow y = -2
$$

✔ Solution: $ (-1, -2) $

→ Matches STARTED → Letter: S

---

#### H)
$$
\begin{align*}
4x + 3y &= 9 \quad \text{(1)}\\
3x + 4y &= 12 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 4:
$$
16x + 12y = 36
$$

Multiply (2) by 3:
$$
9x + 12y = 36
$$

Subtract:
$$
(16x + 12y) - (9x + 12y) = 36 - 36 \Rightarrow 7x = 0 \Rightarrow x = 0
$$

Plug into (1):
$$
4(0) + 3y = 9 \Rightarrow 3y = 9 \Rightarrow y = 3
$$

✔ Solution: $ (0, 3) $

→ Matches AND → Letter: A

---

#### I)
$$
\begin{align*}
5x - 3y &= 16 \quad \text{(1)}\\
4x + 5y &= -2 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 5:
$$
25x - 15y = 80
$$

Multiply (2) by 3:
$$
12x + 15y = -6
$$

Add:
$$
(25x - 15y) + (12x + 15y) = 80 - 6 \Rightarrow 37x = 74 \Rightarrow x = 2
$$

Plug into (1):
$$
5(2) - 3y = 16 \Rightarrow 10 - 3y = 16 \Rightarrow -3y = 6 \Rightarrow y = -2
$$

✔ Solution: $ (2, -2) $

→ Matches SELLING → Letter: E

---

#### J)
$$
\begin{align*}
4x - 3y &= -20 \quad \text{(1)}\\
-x - 8y &= 5 \quad \text{(2)}
\end{align*}
$$

Multiply (2) by 4:
$$
-4x - 32y = 20
$$

Add to (1):
$$
(4x - 3y) + (-4x - 32y) = -20 + 20 \Rightarrow -35y = 0 \Rightarrow y = 0
$$

Plug into (2):
$$
-x - 8(0) = 5 \Rightarrow -x = 5 \Rightarrow x = -5
$$

✔ Solution: $ (-5, 0) $

→ Matches BUTTER → Letter: B

---

#### K)
$$
\begin{align*}
-3x + 7y &= -1 \quad \text{(1)}\\
-2x + 5y &= 0 \quad \text{(2)}
\end{align*}
$$

Multiply (1) by 2:
$$
-6x + 14y = -2
$$

Multiply (2) by 3:
$$
-6x + 15y = 0
$$

Subtract:
$$
(-6x + 15y) - (-6x + 14y) = 0 - (-2) \Rightarrow y = 2
$$

Plug into (2):
$$
-2x + 5(2) = 0 \Rightarrow -2x + 10 = 0 \Rightarrow x = 5
$$

✔ Solution: $ (5, 2) $

→ Matches CHEEP → Letter: C

---

#### L)
$$
\begin{align*}
5x + 6y &= -11 \quad \text{(1)}\\
3x + y &= -4 \quad \text{(2)}
\end{align*}
$$

Multiply (2) by 6:
$$
18x + 6y = -24
$$

Subtract (1):
$$
(18x + 6y) - (5x + 6y) = -24 - (-11) \Rightarrow 13x = -13 \Rightarrow x = -1
$$

Plug into (2):
$$
3(-1) + y = -4 \Rightarrow -3 + y = -4 \Rightarrow y = -1
$$

✔ Solution: $ (-1, -1) $

→ Matches BEEF → Letter: B

---

🧩 Now, collect the letters from each solution:

| System | Solution | Word Matched | Letter |
|--------|----------|--------------|--------|
| A | (2,3) | BIRDSEED | B |
| B | (1,-2) | SINGING | S |
| C | (1,-4) | WHO | W |
| D | (-2,4) | MOO | M |
| E | (2,1) | TWEET | T |
| F | (1,4) | FARMER | F |
| G | (-1,-2) | STARTED | S |
| H | (0,3) | AND | A |
| I | (2,-2) | SELLING | E |
| J | (-5,0) | BUTTER | B |
| K | (5,2) | CHEEP | C |
| L | (-1,-1) | BEEF | B |

Now, fill in the blanks based on the order of the letters in the puzzle.

The top box says:

> A The B Farmer C who D Fed E his F cows G birdseed H and I started J selling K cheep L milk?

Wait — actually, look at the original layout:

It says:
```
A B C D E F
The Farmer who Fed his cows
G H I J K L
birdseed and started selling cheep milk?
```

So the words are:

- A: The → letter from A → B
- B: Farmer → from B → S
- C: who → from C → W
- D: Fed → from D → M
- E: his → from E → T
- F: cows → from F → F
- G: birdseed → from G → S
- H: and → from H → A
- I: started → from I → E
- J: selling → from J → B
- K: cheep → from K → C
- L: milk → from L → B

So plug in:

> B S W M T F S A E B C B

But this doesn’t make sense. Wait — perhaps we need to look at the answers and see which word matches the solution, and use the first letter of the word to fill in the blank.

Wait — no! Let’s re-read the instructions:

> "Find the solution in the answer column and notice the word next to it. Write this word in the box containing the letter of that exercise."

Ah! So:

- Each problem has a solution.
- That solution matches a word in the answer column.
- That word is what you write in the box with the letter of the problem.

For example:

- Problem A has solution (2,3) → matches BIRDSEED → so write BIRDSEED in box A.
- Problem B has solution (1,-2) → matches SINGING → write SINGING in box B.
- etc.

Then, read across the boxes to get the joke.

So let’s do that.

---

✔ Final Answer (Fill in the boxes):

| Box | Word to Write |
|-----|----------------|
| A | BIRDSEED |
| B | SINGING |
| C | WHO |
| D | MOO |
| E | TWEET |
| F | FARMER |
| G | STARTED |
| H | AND |
| I | SELLING |
| J | BUTTER |
| K | CHEEP |
| L | BEEF |

Now, go back to the sentence:

> A The B Farmer C who D Fed E his F cows G birdseed H and I started J selling K cheep L milk?

Wait — but the words we found are not matching the positions.

Wait — the structure is:

```
A [ ] B [ ] C [ ] D [ ] E [ ] F [ ]
The Farmer who Fed his cows
G [ ] H [ ] I [ ] J [ ] K [ ] L [ ]
birdseed and started selling cheep milk?
```

So we must replace each letter with the word associated with that problem.

So:

- A → BIRDSEED
- B → SINGING
- C → WHO
- D → MOO
- E → TWEET
- F → FARMER
- G → STARTED
- H → AND
- I → SELLING
- J → BUTTER
- K → CHEEP
- L → BEEF

Now, plug into the sentence:

> BIRDSEED The SINGING Farmer WHO Fed MOO his TWEET cows STARTED birdseed AND SELLING BUTTER CHEEP BEEF milk?

That’s not making sense.

Wait — maybe we misunderstood.

Let’s reread the instructions:

> "Find the solution in the answer column and notice the word next to it. Write this word in the box containing the letter of that exercise."

And the answer column has:

```
TWEET (1,2)
HIS (2,1)
SELLING (-5,0)
BIRDSEED (-1,-2)
UDDER (2,0)
THE (2,3)
SINGING (-5,4)
STARTED (2,-2)
FED (-2,4)
BUTTER (-1,3)
COWS (1,4)
MILK (-1,-1)
FARMER (1,-2)
AND (0,3)
WINGS (2,-4)
WHO (1,-4)
MOO (1,3)
CHEEP (5,2)
BEEF (3,-2)
```

So now, for each problem, we find its solution and match it to the word.

Let’s list them again:

| Problem | Solution | Matching Word |
|--------|----------|---------------|
| A | (2,3) | THE |
| B | (1,-2) | FARMER |
| C | (1,-4) | WHO |
| D | (-2,4) | FED |
| E | (2,1) | HIS |
| F | (1,4) | COWS |
| G | (-1,-2) | BIRDSEED |
| H | (0,3) | AND |
| I | (2,-2) | STARTED |
| J | (-5,0) | SELLING |
| K | (5,2) | CHEEP |
| L | (-1,-1) | MILK |

Now, go back to the sentence:

> A The B Farmer C who D Fed E his F cows G birdseed H and I started J selling K cheep L milk?

So:

- A → THE
- B → FARMER
- C → WHO
- D → FED
- E → HIS
- F → COWS
- G → BIRDSEED
- H → AND
- I → STARTED
- J → SELLING
- K → CHEEP
- L → MILK

Now fill in:

> THE The FARMER Farmer WHO who FED Fed HIS his COWS cows BIRDSEED birdseed AND and STARTED started SELLING selling CHEEP cheep MILK milk?

Wait — that’s redundant.

But the original sentence is:

> A The B Farmer C who D Fed E his F cows G birdseed H and I started J selling K cheep L milk?

So replacing:

- A: THE → "THE"
- B: FARMER → "Farmer"
- C: WHO → "who"
- D: FED → "Fed"
- E: HIS → "his"
- F: COWS → "cows"
- G: BIRDSEED → "birdseed"
- H: AND → "and"
- I: STARTED → "started"
- J: SELLING → "selling"
- K: CHEEP → "cheep"
- L: MILK → "milk"

So full sentence becomes:

> THE The FARMER Farmer WHO who FED Fed HIS his COWS cows BIRDSEED birdseed AND and STARTED started SELLING selling CHEEP cheep MILK milk?

That’s awkward.

Wait — probably the original sentence is just a placeholder, and the actual joke is formed by reading the words in order A through L.

So the joke is:

> THE FARMER WHO FED HIS COWS BIRDSEED AND STARTED SELLING CHEEP MILK?

But “cheep” is a pun on “cheap”.

So the punchline is:

> "The farmer who fed his cows birdseed and started selling cheep milk?"

“Cheep” sounds like “cheap”, so it’s a pun.

But why does it say “Did you hear about...”?

Ah! It’s a joke:

> Did you hear about the farmer who fed his cows birdseed and started selling cheep milk?

That’s funny because birds eat birdseed, not cows — and “cheep” is a sound a chick makes, so “cheep milk” is nonsense.

So the joke is:

> Did you hear about the farmer who fed his cows birdseed and started selling cheep milk?

Which is a play on “cheap milk” — but he’s selling “cheep” (like a chicken sound) milk.

So the final answer is:

> THE FARMER WHO FED HIS COWS BIRDSEED AND STARTED SELLING CHEEP MILK?

With the words:

- A: THE
- B: FARMER
- C: WHO
- D: FED
- E: HIS
- F: COWS
- G: BIRDSEED
- H: AND
- I: STARTED
- J: SELLING
- K: CHEEP
- L: MILK

✔ All match.

---

✔ Final Answer:

> Did you hear about the farmer who fed his cows birdseed and started selling cheep milk?

This is a pun on "cheap milk" — "cheep" sounds like a chicken noise, and cows don't eat birdseed!

---

📌 Summary of Solutions:

| Problem | Solution | Word |
|--------|---------|------|
| A | (2,3) | THE |
| B | (1,-2) | FARMER |
| C | (1,-4) | WHO |
| D | (-2,4) | FED |
| E | (2,1) | HIS |
| F | (1,4) | COWS |
| G | (-1,-2) | BIRDSEED |
| H | (0,3) | AND |
| I | (2,-2) | STARTED |
| J | (-5,0) | SELLING |
| K | (5,2) | CHEEP |
| L | (-1,-1) | MILK |

And the joke is:

> Did you hear about the farmer who fed his cows birdseed and started selling cheep milk?