Understanding Solutions of Two-Variable Equations
Understanding solutions of two-variable equations is a Grade 7 math skill from Yoshiwara Intermediate Algebra. A solution to an equation in x and y is an ordered pair (x, y) that makes the equation true, and all such solutions form the graph of the equation.
Key Concepts
Property An equation in two variables, such as $y = 4x 2$, has many solutions. Each solution consists of an ordered pair of values, one for $x$ and one for $y$, that together satisfy the equation (make the equation true.).
The ordered pair $(1, 3)$ is not a solution of $y = 4x 2$ because substituting the values gives $4(1) 2 = 2$. Since the y value is 3, and $3 \ne 2$, the pair is not a solution.
Common Questions
What is a solution to a two-variable equation?
A solution is an ordered pair (x, y) that, when substituted into the equation, makes it a true statement. For example, (2, 5) is a solution to y = 2x + 1.
How many solutions does a linear equation in two variables have?
A linear equation in two variables has infinitely many solutions — all the points lying on the line it represents.
How do you check if an ordered pair is a solution?
Substitute the x and y values into the equation and check if both sides are equal. If they are, the ordered pair is a solution.
What is the graph of all solutions to a two-variable equation?
The graph of all solutions is the curve or line that satisfies the equation. For a linear equation, this is a straight line.