Fill in the justification blanks to the following proof:
Given: 4x – 6y = -8; x = 10
Prove: y = 8
Statements: Reasons:
1. 4(10) - 6y = -8 Given
2. 40 - 6y = -8 Substitution
3. -6y = -8 - 40 Simplification
4. -6y = -48 Simplification
5. y = (-48)/(-6) Division Property of Equality
6. y = 8 Simplification
To prove: y = 8
1. Given: 4x - 6y = -8
2. Substitute x = 10 into the equation: 4(10) - 6y = -8
3. Simplify: 40 - 6y = -8
4. Subtract 40 from both sides: -6y = -48
5. Divide both sides by -6: y = (-48)/(-6)
6. Simplify: y = 8
Therefore, we have proven that y = 8.
To prove y = 8, we can substitute the value of x into the given equation and solve for y.
Given: 4x – 6y = -8; x = 10
Step 1: Substitute x = 10 into the equation:
4(10) – 6y = -8
Simplifying the equation:
40 - 6y = -8
Step 2: Solve for y:
40 - 6y = -8
Subtract 40 from both sides:
-6y = -8 - 40
-6y = -48
Step 3: Divide both sides by -6:
-6y / -6 = -48 / -6
y = 8
Therefore, we have proven that y = 8 by substituting the given value of x into the equation.