Certainly! Let's go through each statement and carefully address what it is referring to.
1. Substitution Property of Equality:
- Statement: "The [tex]$\qquad$[/tex] states that if [tex]\( x = y \)[/tex], then [tex]\( y \)[/tex] can be substituted for [tex]\( x \)[/tex] in any expression."
- Explanation: This property is fundamental in algebra and states that if two quantities are equal, they can replace each other in any equation or expression without changing the truth value of that expression. This is called the substitution property of equality.
2. Linear Equation:
- Statement: "A [tex]$\qquad$[/tex] is an equation in which each term is either a constant or the product of a constant and a single variable."
- Explanation: In mathematics, equations are often classified by the types of terms that appear in them. An equation where each term is either a constant (a number on its own) or a product of a constant and a single variable (like [tex]\(2x\)[/tex] or [tex]\(-3y\)[/tex]) is known as a linear equation. Linear equations form straight lines when graphed on a coordinate plane.
3. Linear Inequality:
- Statement: "A [tex]$\qquad$[/tex] is an inequality in which each term is either a constant or the product of a constant and a single variable."
- Explanation: Similar to linear equations, inequalities compare expressions to determine which is larger, smaller, or if they are not equal. If each term in the inequality follows the same rule—being either a constant or the product of a constant and a single variable—the inequality is termed as a linear inequality. Linear inequalities represent half-planes when graphed in the coordinate plane.
Putting all this together, we have:
1. The substitution property of equality states that if [tex]\( x = y \)[/tex], then [tex]\( y \)[/tex] can be substituted for [tex]\( x \)[/tex] in any expression.
2. A linear equation is an equation in which each term is either a constant or the product of a constant and a single variable.
3. A linear inequality is an inequality in which each term is either a constant or the product of a constant and a single variable.
