Keystone Algebra: Module 1 Practice

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.

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

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

The quadratic formula is $$x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$$ , used to find the roots of a quadratic equation of the form $$ax^2 + bx + c = 0$$ .

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

Combine like terms: $$3x^2 + 2x - 8 + x^2 - 6x - 4 = 4x^2 - 4x - 12$$ .

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.

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.

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

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