Solving Systems of Equations by Graphing & Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

How do you graph a linear equation?

Back

By plotting points that satisfy the equation and connecting them to form a line.

Front

What is the point of intersection in a graph of two equations?

Back

The point where the two lines meet, representing the solution to the system of equations.

Front

What does it mean if two lines are parallel?

Back

They have no points of intersection, indicating that the system has no solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solution, typically represented by parallel lines.

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What is a consistent system of equations?

Back

A system that has at least one solution, which can be either one solution or infinitely many solutions.

Front

What does it mean if two lines coincide?

Back

They lie on top of each other, indicating that the system has infinitely many solutions.

Front

How do you determine if a point is a solution to a system of equations?

Back

By substituting the point's coordinates into each equation to see if they hold true.