Example Card: Verifying a Solution
Check solutions to equations and systems by substituting values back into original equations to confirm both sides are equal in Grade 9 Algebra.
Key Concepts
A point might solve one equation, but does it solve the whole system? Let's check. This card highlights the key idea of verifying if an ordered pair is a solution to a system of equations.
Example Problem Tell whether the ordered pair $(5, 1)$ is a solution of the system: $2x + 3y = 13$, $x = 8 2y$.
Step by Step 1. To verify, we substitute $5$ for $x$ and $1$ for $y$ in each equation and check if the statements are true. 2. We check the first equation, $2x + 3y = 13$: $$2(5) + 3(1) \stackrel{?}{=} 13$$ $$10 + 3 \stackrel{?}{=} 13$$ $$13 = 13 \quad \checkmark$$ The ordered pair works in the first equation. 3. Now we check the second equation, $x = 8 2y$: $$5 \stackrel{?}{=} 8 2(1)$$ $$5 \stackrel{?}{=} 8 2$$ $$5 \neq 6 \quad X$$ The ordered pair does not work in the second equation. 4. Since the ordered pair $(5, 1)$ only makes one equation true, it is not a solution to the entire system.
Common Questions
What is Example Card: Verifying a Solution?
Example Card: Verifying a Solution is a key concept in Grade 9 math. It involves applying specific rules and properties to simplify expressions, solve equations, or analyze mathematical relationships. Understanding this topic builds foundational skills needed for higher-level algebra and beyond.
How is Example Card: Verifying a Solution used in real-world applications?
Example Card: Verifying a Solution appears in practical contexts such as financial calculations, engineering problems, and data analysis. Mastering this skill helps students model and solve problems they will encounter in science, technology, and everyday decision-making situations.
What are common mistakes when working with Example Card: Verifying a Solution?
Common errors include forgetting to apply rules to all terms, sign errors when working with negatives, and skipping verification steps. Always double-check by substituting answers back into the original problem and reviewing each algebraic step carefully.