Question

The following proof shows an equivalent system of equations created from another system of equations. Fill in the missing reason in the proof.

1) a multiplication property of equality
2) addition property of equality
3) division property of equality
4) subtraction property of equality

Answer 1

The missing reason in the proof is the multiplication property of equality. By multiplying both sides of the equation by the same number, each term on both sides is multiplied by that number. Therefore, the equivalent system of equations is obtained.

Step-by-step explanation:

The missing reason in the proof is the multiplication property of equality.

1. Start with the equation 2A = B.
2. Multiply both sides of the equation by ½.
3. By the multiplication property of equality, each term on both sides of the equation is multiplied by ½.
4. On the left side, 2A × ½ = A.
5. On the right side, B × ½ = ½B.
6. So, the equivalent system of equations is A = ½B