Example Card: Verifying a Solution
Verify solutions to algebraic equations in Grade 9. Substitute the answer back into the original equation, confirm both sides are equal, and identify any extraneous solutions.
Key Concepts
Let's test a point to see if it's the true key that unlocks both locks in our system. This first key idea is about verifying if a given point is a solution.
Example Problem.
Tell whether the ordered pair $(3, 1)$ is a solution of the system $2x + 3y = 9$ and $x = 4y 1$.
Common Questions
How do you verify a solution to an algebraic equation?
Substitute the solution value back into the original equation. Evaluate both sides separately. If they produce the same number, the solution is verified as correct.
Why is verifying solutions important in algebra?
Verification catches arithmetic errors and identifies extraneous solutions — values that satisfy a transformed equation but not the original, common with absolute value and rational equations.
What is an extraneous solution?
An extraneous solution satisfies a modified equation but not the original. These appear especially after squaring both sides or clearing denominators. Always check solutions by substituting into the original.