Systems of Equations- graphing and substitution flashcard

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 graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, indicating no solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other, indicating infinitely many solutions.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

How do you determine if a system has one solution?

Back

If the lines intersect at exactly one point.

Front

What is the slope-intercept form of a line?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a graph?

Back

It is the point where the line crosses the y-axis.