Keystone Algebra: Module 1 Practice

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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How do you solve a system of equations using substitution?

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1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

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What does it mean for two variables to be directly proportional?

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Two variables are directly proportional if they increase or decrease at the same rate, meaning their ratio is constant.

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What is the quadratic formula?

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What is the difference between an expression and an equation?

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An expression is a combination of numbers and variables without an equality sign, while an equation states that two expressions are equal.

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What is an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

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How do you graph a linear inequality?

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1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.

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What does it mean to simplify a radical expression?

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To simplify a radical expression means to rewrite it in its simplest form, removing any perfect squares from under the radical sign.

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What is the relationship between the coefficients and the roots of a polynomial?

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The coefficients of a polynomial can provide information about the roots, such as their sum and product, according to Vieta's formulas.