Which of the following equations have a solution of z = 3 ?

Question

​
​Select the TWO correct equations.(2 points)
Responses

5z + 40 = 62
5z + 40 = 62

9z − 5 = 22
9z − 5 = 22

9z + 22 = 26
9z + 22 = 26

54 − 8z = 30

Answer 1

To determine which of the given equations has a solution of \( z = 3 \), we will substitute \( z = 3 \) into each equation and check if the equation holds true.

1. Equation: \( 5z + 40 = 62 \)
   Substituting \( z = 3 \): \[ 5(3) + 40 = 15 + 40 = 55 \quad (\text{not } 62) \] This equation does not have a solution of \( z = 3 \).

2. Equation: \( 9z - 5 = 22 \)
   Substituting \( z = 3 \): \[ 9(3) - 5 = 27 - 5 = 22 \quad (\text{equals } 22) \] This equation has a solution of \( z = 3 \).

3. Equation: \( 9z + 22 = 26 \)
   Substituting \( z = 3 \): \[ 9(3) + 22 = 27 + 22 = 49 \quad (\text{not } 26) \] This equation does not have a solution of \( z = 3 \).

4. Equation: \( 54 - 8z = 30 \)
   Substituting \( z = 3 \): \[ 54 - 8(3) = 54 - 24 = 30 \quad (\text{equals } 30) \] This equation has a solution of \( z = 3 \).

Correct Equations:

1. \( 9z - 5 = 22 \)
2. \( 54 - 8z = 30 \)

So, the two correct equations are:

• \( 9z - 5 = 22 \)
• \( 54 - 8z = 30 \)