Check If `(X,Y)` Satisfies The Equation Worksheet

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Check if `(x,y)` satisfies the equation is about seeing if a given point `(x,y)` fits into a certain equation. We do this by putting the values of `x` and `y` into the equation and seeing if both sides match. If they do, the point works in the equation; if not, it doesn't. This helps us confirm solutions, draw graphs correctly, and understand how numbers relate in math problems.

Algebra 1

Linear Relationship

How Will This Worksheet on "Check If `(x,y)` Satisfies the Equation" Benefit Your Student's Learning?

Enhances understanding of how to apply mathematical concepts in problem-solving situations.
Reinforces accuracy by providing a method to double-check solutions.
Improves graphing skills by ensuring plotted points align with the equation.
Deepens comprehension of relationships between variables in equations.
Builds confidence in tackling more complex mathematical proble...

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Solved Example

Q. Is

(0, 3)

a solution to the equation

y = 6x

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Solution:

Understand Solution Criteria: Understand what it means for a point to be a solution to an equation. $\newline$ A point is a solution to an equation if, when the $x$ and $y$ values of the point are substituted into the equation, the equation is satisfied (both sides are equal).
Substitute Values: Substitute the $x$ and $y$ values of the point $(0, 3)$ into the equation $y = 6x$ . $\newline$ Substitute $x = 0$ and $y = 3$ into the equation to see if it holds true. $\newline$ $3 = 6 \times 0$
Perform Multiplication: Perform the multiplication on the right side of the equation. $6 \times 0 = 0$
Compare Results: Compare the results of the substitution to the original equation. $\newline$ After substitution and calculation, we have $3 = 0$ , which is not true.
Determine Solution Status: Determine if the point $(0, 3)$ is a solution to the equation. $\newline$ Since $3$ does not equal $0$ , the point $(0, 3)$ is not a solution to the equation $y = 6x$ .

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