Math Problem Statement
Is the ordered pair (1/2, 5/4) a solution of the equation 3x - 2y = 2? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Solution
The image contains a problem asking whether a given ordered pair is a solution to a system of equations. Let's work through the solution based on the information visible.
Problem Description:
You are given a system of equations and asked to verify if the ordered pair is a solution.
The system of equations is:
3x - 2y &= 2 \\ 5x + y &= 6 \end{aligned}$$ The ordered pair is $$\left( \frac{1}{2}, \frac{5}{4} \right)$$. ### Steps to Verify: 1. **Substitute $$x = \frac{1}{2}$$ and $$y = \frac{5}{4}$$ into the first equation:** $$3\left(\frac{1}{2}\right) - 2\left(\frac{5}{4}\right) = 2$$ Simplify: $$\frac{3}{2} - \frac{10}{4} = \frac{3}{2} - \frac{5}{2} = -\frac{2}{2} = -1$$ Since $$-1 \neq 2$$, the ordered pair is **not** a solution to the first equation. 2. **Conclusion:** Since the pair doesn't satisfy the first equation, it cannot be a solution to the system of equations. Thus, the answer to the problem is that the ordered pair does **not** satisfy the given system of equations. ### Would you like further details or any clarifications? Here are some related questions you might find useful: 1. What happens if one equation is satisfied but not the other? 2. How do you solve a system of equations algebraically? 3. How can graphing help verify solutions to systems of equations? 4. How do substitution and elimination methods work in solving systems? 5. What does it mean geometrically if a pair is not a solution? **Tip:** When verifying solutions for systems of equations, always substitute the values into both equations to check consistency.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Substitution Method
Formulas
Substitute x and y into the equation: 3x - 2y = 2
Theorems
None
Suitable Grade Level
Grades 6-8
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