Math Problem Statement

Which ordered pair is a solution of the equation? [ 7x-5=4y-6] Choose 1 answer: Choose 1 answer: (Choice A) Only [(2,4)] A Only [(2,4)] (Choice B) Only [(3,6)] B Only [(3,6)] (Choice C) Both [(2,4)] and [(3,6)] C Both [(2,4)] and [(3,6)]

Solution

To determine which ordered pair is a solution to the equation 7x5=4y67x - 5 = 4y - 6, let's test each pair by substituting xx and yy values.

Step 1: Substitute (2,4)(2, 4)

For x=2x = 2 and y=4y = 4: 7(2)5=4(4)67(2) - 5 = 4(4) - 6 Calculating each side: 145=16614 - 5 = 16 - 6 9=10(False)9 = 10 \quad (\text{False}) So, (2,4)(2, 4) is not a solution.

Step 2: Substitute (3,6)(3, 6)

For x=3x = 3 and y=6y = 6: 7(3)5=4(6)67(3) - 5 = 4(6) - 6 Calculating each side: 215=24621 - 5 = 24 - 6 16=18(False)16 = 18 \quad (\text{False}) So, (3,6)(3, 6) is not a solution either.

Conclusion

Since neither (2,4)(2, 4) nor (3,6)(3, 6) satisfies the equation, the correct answer is actually that neither pair is a solution. However, based on the given choices, none of the options match this outcome directly.

If you'd like further assistance or have questions, feel free to ask!


Here are 5 related questions for practice:

  1. Can you identify solutions to the equation 3x+4=2y53x + 4 = 2y - 5?
  2. What happens if you try x=1x = -1 and y=1y = 1 in the equation 7x5=4y67x - 5 = 4y - 6?
  3. What is the slope-intercept form of 7x5=4y67x - 5 = 4y - 6?
  4. How would you graph the equation 7x5=4y67x - 5 = 4y - 6?
  5. What are ordered pairs that satisfy y=2x+3y = 2x + 3?

Tip: When verifying if a pair is a solution, always substitute both values and check if the equation holds true.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations
Substitution

Formulas

Linear equation format \( ax + by = c \)

Theorems

Solution verification of linear equations by substitution

Suitable Grade Level

Grades 7-8