Math Problem Statement

consider the equation 2x-7y=5. Solve the equation for x in terms of y.

Solution

To solve the equation 2x7y=52x - 7y = 5 for xx in terms of yy, follow these steps:

  1. Start with the original equation: 2x7y=52x - 7y = 5

  2. Isolate 2x2x by adding 7y7y to both sides: 2x=7y+52x = 7y + 5

  3. Divide both sides of the equation by 2 to solve for xx: x=7y+52x = \frac{7y + 5}{2}

Thus, the solution for xx in terms of yy is: x=7y+52x = \frac{7y + 5}{2}

Would you like a more detailed explanation, or do you have any questions about the steps?


Here are 5 related questions to explore:

  1. What would the value of xx be if y=2y = 2?
  2. How can you rewrite the equation 2x7y=52x - 7y = 5 in slope-intercept form?
  3. How would you solve for yy in terms of xx from the equation 2x7y=52x - 7y = 5?
  4. What is the significance of the slope of the equation in a linear graph?
  5. If the equation were instead 2x7y=102x - 7y = 10, how would the solution for xx change?

Tip: When solving linear equations, isolating one variable first can simplify the process greatly.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Solving for a Variable

Formulas

Linear equation: 2x - 7y = 5

Theorems

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Suitable Grade Level

Grades 8-10