Lesson Flashcard 4.3 Day 2: 3x3 Systems

Front

What is a system of equations?

Back

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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What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical method for solving a system of equations?

Back

The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

How do you determine the number of solutions in a system of equations?

Back

The number of solutions can be determined by analyzing the slopes and intercepts of the equations: parallel lines (no solution), intersecting lines (one solution), or the same line (infinitely many solutions).

Front

What is the role of coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.