Math  /  Algebra

QuestionWhat value of yy is a solution to ais a 61=7y1661=7 y-16 y=11y=11 y=12y=12

Studdy Solution

STEP 1

1. We are given the linear equation 61=7y1661 = 7y - 16.
2. We need to solve for the variable yy.
3. We are provided with potential solutions: y=11y = 11 and y=12y = 12.

STEP 2

1. Rearrange the given equation to isolate yy.
2. Substitute the potential solutions into the equation to verify which one satisfies it.

STEP 3

Rearrange the equation 61=7y1661 = 7y - 16 to isolate yy:
61+16=7y 61 + 16 = 7y

STEP 4

Combine like terms:
77=7y 77 = 7y

STEP 5

Solve for yy by dividing both sides of the equation by 7:
y=777 y = \frac{77}{7}

STEP 6

Simplify the division to find yy:
y=11 y = 11

STEP 7

Verify the solution by substituting y=11y = 11 back into the original equation:
61=7(11)16 61 = 7(11) - 16

STEP 8

Calculate the right-hand side:
61=7716 61 = 77 - 16

STEP 9

Combine like terms to verify the equality:
61=61 61 = 61

STEP 10

Verify the other potential solution y=12y = 12 by substituting it back into the original equation:
61=7(12)16 61 = 7(12) - 16

STEP 11

Calculate the right-hand side for y=12y = 12:
61=8416 61 = 84 - 16

STEP 12

Combine like terms to check the equality:
6168 61 \neq 68
_SOLUTION_: The solution to the equation 61=7y1661 = 7y - 16 is y=11y = 11.

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