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Question

Difficulty: EasyLinear Equations in Two Variables

If 3x−2(y−5)=123x - 2(y - 5) = 12 and x=8x = 8, what is the value of yy?

  1. A
    1
  2. B
    6
  3. 11Answer
  4. D
    10

Answer

11
The correct answer is 11. Substituting x=8x = 8 into the equation gives 3(8)−2(y−5)=123(8) - 2(y - 5) = 12, which simplifies to 24−2y+10=1224 - 2y + 10 = 12. Combining the constants on the left side yields 34−2y=1234 - 2y = 12. Subtracting 34 from both sides gives −2y=−22-2y = -22. Finally, dividing both sides by −2-2 yields y=11y = 11.

Step-by-Step Solution

1
Substitute x=8x = 8 into the given equation.
3(8)−2(y−5)=123(8) - 2(y - 5) = 12, which simplifies to 24−2(y−5)=1224 - 2(y - 5) = 12.
This isolates the variable yy by replacing the variable xx with its given value.
2
Distribute −2-2 to the terms inside the parentheses.
24−2y+10=1224 - 2y + 10 = 12.
Multiplying −2-2 by yy gives −2y-2y, and multiplying −2-2 by −5-5 gives +10+10 because the product of two negative numbers is positive.
3
Combine the constant terms on the left side of the equation and subtract the result from both sides.
34−2y=12⇒−2y=−2234 - 2y = 12 \Rightarrow -2y = -22.
Combining 2424 and 1010 gives 3434. Subtracting 3434 from both sides isolates the variable term −2y-2y.
4
Divide both sides by −2-2 to solve for yy.
y=11y = 11.
Dividing both sides of the equation by the coefficient of the variable term isolates the variable.

Key Concept

Solving linear equations in two variables by substitution and isolation.
Estimated Time:45s
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Topics

Linear Equations in Two Variables

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