which equaction has no solution select all that apply
8k+38=-3(-6-4k)
36-7y=-7(y-5)
Both equations have solutions.
To determine which equation has no solution, we need to solve each equation separately and see if we reach a contradiction.
1) For the equation 8k + 38 = -3(-6 - 4k):
Step 1: Distribute -3 to -6 and -4k:
8k + 38 = 18 + 12k
Step 2: Combine like terms:
-4k = -20
Step 3: Divide by -4:
k = 5
Since the equation has a solution (k = 5), it does not satisfy the condition of having no solution.
2) For the equation 36 - 7y = -7(y - 5):
Step 1: Distribute -7 to y and -5:
36 - 7y = -7y + 35
Step 2: Simplify the equation:
36 = 35
We see that the equation contradicts itself (36 ≠ 35). Therefore, this equation has no solution.
In conclusion, the equation 36 - 7y = -7(y - 5) has no solution.
To determine which equation has no solution, we can solve each equation and see if a solution exists.
1. 8k + 38 = -3(-6 - 4k)
To solve this equation, we'll first distribute -3 to both terms inside the bracket:
8k + 38 = 18 + 12k
Next, we'll combine like terms:
8k - 12k = 18 - 38
-4k = -20
To isolate the variable k, we'll divide both sides of the equation by -4:
k = -20 / -4
k = 5
Therefore, equation 8k + 38 = -3(-6 - 4k) has a solution, k = 5.
2. 36 - 7y = -7(y - 5)
To solve this equation, we'll distribute -7 to both terms inside the bracket:
36 - 7y = -7y + 35
Next, we'll add 7y to both sides of the equation:
36 = 35
Since we have a contradiction (36 = 35 is not a true statement), this equation has no solution.
Therefore, the equation 36 - 7y = -7(y - 5) has no solution.
In conclusion, the equation that has no solution is 36 - 7y = -7(y - 5).