Linear Equations in Two Variables

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Questions and Answers

What are two examples of linear equations in two variables?

2x + 3y = 5, x - 2y - 3 = 0

Define a solution of a linear equation in two variables.

A solution of a linear equation is a viable pair of values, one for x and the other for y, which makes the two sides of the equation equal.

How can you determine if a given pair of values is a solution to a linear equation?

Substitute the values into the equation and check if the left-hand side (LHS) equals the right-hand side (RHS).

What makes an equation a linear equation in two variables?

<p>An equation is a linear equation in two variables if it can be put in the form ax + by + c = 0, where a, b, and c are real numbers and a and b are not both zero.</p> Signup and view all the answers

Explain the significance of a² + b² ≠ 0 in the context of linear equations in two variables.

<p>a² + b² ≠ 0 ensures that the equation is not degenerate, meaning it represents a valid linear equation.</p> Signup and view all the answers

Why is x = 1 and y = 7 not a solution to the equation 2x + 3y = 5?

<p>Because when substituted, LHS = 2(1) + 3(7) = 2 + 21 = 23, which is not equal to the RHS.</p> Signup and view all the answers

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