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Questions and Answers
¿Cuál es la característica principal de un sistema de ecuaciones independiente?
¿Cuál es la propiedad de la adición real que establece que el orden de los sumandos no cambia el resultado?
¿Cuál es la forma estándar de una ecuación lineal?
¿Cuál es la forma de una ecuación cuadrática?
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¿Qué método se utiliza para resolver un sistema de ecuaciones eliminando una variable?
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¿Cuál es la propiedad de la multiplicación real que establece que a × 1 = a?
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Study Notes
Systems of Equations
- A system of equations is a set of two or more equations that must be satisfied simultaneously.
- Types of systems:
- Independent systems: have a unique solution.
- Dependent systems: have infinitely many solutions.
- Inconsistent systems: have no solution.
- Methods for solving systems:
- Substitution method: solving one equation for a variable and substituting into the other equation.
- Elimination method: adding or subtracting equations to eliminate a variable.
Real Number Properties
- Properties of real numbers:
- Commutative property of addition: a + b = b + a
- Associative property of addition: (a + b) + c = a + (b + c)
- Distributive property: a(b + c) = ab + ac
- Additive identity: a + 0 = a
- Additive inverse: a + (-a) = 0
- Multiplicative identity: a × 1 = a
- Multiplicative inverse: a × (1/a) = 1 (for non-zero a)
Linear Equations
- A linear equation is an equation in which the highest power of the variable(s) is 1.
- Standard form: ax + by = c, where a, b, and c are constants.
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
- Solving linear equations:
- Addition and subtraction
- Multiplication and division
- Graphing
Quadratic Equations
- A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
- Types of quadratic equations:
- Factored form: (x - r)(x - s) = 0, where r and s are roots.
- Vertex form: a(x - h)^2 + k = 0, where (h, k) is the vertex.
- Solving quadratic equations:
- Factoring
- Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Graphing
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Description
Test your understanding of algebra basics, including systems of equations, real number properties, linear equations, and quadratic equations.
