two-variables linear equations (x=d) Math Worksheets, Math ... - Free Printable

You're given a worksheet titled “Two-Variables Linear Equations (x=d)”, which means each problem gives you a system of two equations, and the first equation is always in the form `ax = b`, so you can solve for `x` directly. Then substitute that value of `x` into the second equation to solve for `y`.

Let’s go through each problem step by step.

---

Problem 1

Equations:
1. `8x = 40`
2. `7x + 4y = 59`

Step 1: Solve for `x` from the first equation:
```
8x = 40
→ x = 40 ÷ 8 = 5
```

Step 2: Plug `x = 5` into the second equation:
```
7(5) + 4y = 59
→ 35 + 4y = 59
→ 4y = 59 - 35 = 24
→ y = 24 ÷ 4 = 6
```

✔ Answer: x = 5, y = 6

---

Problem 2

Equations:
1. `7x = 21`
2. `5x - 4y = 11`

Step 1: Solve for `x`:
```
7x = 21 → x = 3
```

Step 2: Plug into second equation:
```
5(3) - 4y = 11
→ 15 - 4y = 11
→ -4y = 11 - 15 = -4
→ y = (-4) ÷ (-4) = 1
```

✔ Answer: x = 3, y = 1

---

Problem 3

Equations:
1. `7x = 7`
2. `8x - 2y = -8`

Step 1: Solve for `x`:
```
7x = 7 → x = 1
```

Step 2: Plug into second equation:
```
8(1) - 2y = -8
→ 8 - 2y = -8
→ -2y = -8 - 8 = -16
→ y = (-16) ÷ (-2) = 8
```

✔ Answer: x = 1, y = 8

---

Problem 4

Equations:
1. `7x = 35`
2. `2x - 4y = 6`

Step 1: Solve for `x`:
```
7x = 35 → x = 5
```

Step 2: Plug into second equation:
```
2(5) - 4y = 6
→ 10 - 4y = 6
→ -4y = 6 - 10 = -4
→ y = (-4) ÷ (-4) = 1
```

✔ Answer: x = 5, y = 1

---

Problem 5

Equations:
1. `5x = 5`
2. `8x - 2y = 0`

Step 1: Solve for `x`:
```
5x = 5 → x = 1
```

Step 2: Plug into second equation:
```
8(1) - 2y = 0
→ 8 - 2y = 0
→ -2y = -8
→ y = 4
```

✔ Answer: x = 1, y = 4

---

Problem 6

Equations:
1. `2x = 10`
2. `6x + 5y = 45`

Step 1: Solve for `x`:
```
2x = 10 → x = 5
```

Step 2: Plug into second equation:
```
6(5) + 5y = 45
→ 30 + 5y = 45
→ 5y = 15
→ y = 3
```

✔ Answer: x = 5, y = 3

---

Problem 7

Equations:
1. `2x = 10`
2. `2x - 5y = 5`

Step 1: Solve for `x`:
```
2x = 10 → x = 5
```

Step 2: Plug into second equation:
```
2(5) - 5y = 5
→ 10 - 5y = 5
→ -5y = 5 - 10 = -5
→ y = (-5) ÷ (-5) = 1
```

✔ Answer: x = 5, y = 1

---

Problem 8

Equations:
1. `6x = 18`
2. `4x + 6y = 66`

Step 1: Solve for `x`:
```
6x = 18 → x = 3
```

Step 2: Plug into second equation:
```
4(3) + 6y = 66
→ 12 + 6y = 66
→ 6y = 54
→ y = 9
```

✔ Answer: x = 3, y = 9

---

## ✔ Final Answers:

1. x = 5, y = 6
2. x = 3, y = 1
3. x = 1, y = 8
4. x = 5, y = 1
5. x = 1, y = 4
6. x = 5, y = 3
7. x = 5, y = 1
8. x = 3, y = 9

---

## 💡 Explanation Summary:

Each problem gives you a simple linear equation in one variable (`x`) first — this lets you find `x` immediately. Then you plug that `x` value into the second equation (which includes both `x` and `y`) to solve for `y`. This is called the substitution method for solving systems of equations.

This worksheet is designed to help you practice isolating variables and substituting values — foundational skills for algebra!

Let me know if you want to see these graphed or solved using another method! 🎯