Math Problem Statement
For each ordered pair, determine whether it is a solution to the system of equations:
-5x + 4y = 2
3x - 5y = 4
Solution
To determine whether each ordered pair is a solution to the system of equations:
-5x + 4y = 2 \\ 3x - 5y = 4 \end{cases}$$ We substitute the given values of $$x$$ and $$y$$ into both equations and check if both are satisfied. --- ### Ordered Pair 1: $$(6, 8)$$ 1. First equation: $$-5(6) + 4(8) = -30 + 32 = 2$$ → True. 2. Second equation: $$3(6) - 5(8) = 18 - 40 = -22$$ → False. $$(6, 8)$$ is **not a solution**. --- ### Ordered Pair 2: $$(3, 1)$$ 1. First equation: $$-5(3) + 4(1) = -15 + 4 = -11$$ → False. 2. No need to check the second equation as the first fails. $$(3, 1)$$ is **not a solution**. --- ### Ordered Pair 3: $$(-7, 0)$$ 1. First equation: $$-5(-7) + 4(0) = 35 + 0 = 35$$ → False. 2. No need to check the second equation as the first fails. $$(-7, 0)$$ is **not a solution**. --- ### Ordered Pair 4: $$(-4, -4)$$ 1. First equation: $$-5(-4) + 4(-4) = 20 - 16 = 4$$ → False. 2. No need to check the second equation as the first fails. $$(-4, -4)$$ is **not a solution**. --- ### Final Answer: | $$(x, y)$$ | Is it a solution? | |----------------|------------------| | $$(6, 8)$$ | No | | $$(3, 1)$$ | No | | $$(-7, 0)$$ | No | | $$(-4, -4)$$ | No | --- Do you want a detailed explanation for any specific pair or step? Here are 5 follow-up questions to explore further: 1. How do you determine if an ordered pair satisfies a system of equations? 2. What are the methods to solve systems of equations (e.g., substitution, elimination)? 3. Can systems of equations have no solution? 4. How do you graphically check solutions to a system of equations? 5. What happens when a system of equations has infinite solutions? **Tip**: Always substitute the $$x$$ and $$y$$ values into *both* equations to confirm if a pair is a solution.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Substitution Method
Checking Solutions
Formulas
Ax + By = C (Standard form of a linear equation)
Theorems
Solutions of systems of linear equations require satisfying both equations simultaneously.
Suitable Grade Level
Grades 8-10