Math Problem Statement
Which option is not a solution of 2x = 7y = 28? Options: (a) (7, 2), (b) (0, 4), (c) (2, 7), (d) (14, 0)
Solution
The equation given in the image is , which can be interpreted as two separate equations:
-
Solve :
-
Solve :
Thus, the solution to the system of equations is and . Now, we check which of the given options is not a solution:
Option (a) :
- For : Thus, option (a) is not a solution.
Checking the other options:
Option (b) :
- For : So, (b) is also not a solution.
Option (c) :
- For : Thus, (c) is not a solution.
Option (d) :
- For :
- For : Thus, (d) is also not a solution.
However, (a) is the first incorrect one when compared directly to the expected solutions.
Let me know if you want to dive deeper into the explanation or solve further problems.
Follow-up questions:
- How would you graph the equation ?
- How do you test for solutions in a system of linear equations?
- Can you generalize this method for a different equation?
- What are the key steps to solving linear equations in two variables?
- How would this method change if the equation involved fractions?
Tip:
When solving systems of equations, always check each possible solution by substituting the values of both variables to ensure correctness.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Linear equation system: 2x = 28 and 7y = 28
Theorems
System of equations
Suitable Grade Level
Grades 6-9