Write a two column proof.
Given: 7y = 8x - 14; y = 6
Prove: x = 7
42 = 8x - 14
Add 14 to both sides, then divide both sides by 8.
To write a two-column proof, we will list each given statement and reason in two separate columns.
Given:
1. 7y = 8x - 14
2. y = 6 (Given)
To prove:
x = 7
Proof:
| Statement | Reason |
|-----------------|-------------------------------------|
| 1. 7y = 8x - 14 | Given |
| 2. y = 6 | Given |
| 3. 7(6) = 8x - 14 | Substitute y with 6 from statement 2 |
| 4. 42 = 8x - 14 | Simplify 7(6) to 42 |
| 5. 42 + 14 = 8x | Add 14 to both sides |
| 6. 56 = 8x | Simplify 42 + 14 to 56 |
| 7. 56 / 8 = x | Divide both sides by 8 |
| 8. 7 = x | Simplify 56 / 8 to 7 |
Therefore, we have proved that x = 7.