Write a two-column proof
Given: 7y =8x =14; y=6
Prove: x=7
substitute 7 for y
division property (divide by 8)
To prove that x=7, we need to show that both sides of the equation 7y=8x=14 simplify to the same value when y=6.
Given: 7y=8x=14; y=6
Statement | Reason
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1. Given: 7y=8x=14, y=6 | Given
2. Substitute y=6 into 7y=8x=14 | Substitution Property
3. 7(6) = 8x = 14 | Substitute 6 for y
4. 42 = 8x = 14 | Simplify 7(6)
5. 8x = 14 | Transitive Property of Equality
6. 8x = 42 | Commutative Property of Equality
7. Divide equation 8x=42 by 8 | Division Property of Equality
8. x = 7 | Simplify 42/8
9. x = 7 | Reflexive Property of Equality
Therefore, x=7 has been proven.