Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations graphically?

Back

It means to find the point(s) where the graphs of the equations intersect, representing the solution(s) to the system.

Front

What is substitution in solving systems of equations?

Back

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

Front

What is the elimination method in solving systems of equations?

Back

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

Front

What does the slope of a line represent in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes; it is the ratio of the rise over the run.

Front

How do you find the slope from the equation y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

It means they have the same slope and will never intersect, indicating no solution to the system.

Front

What does it mean if two lines intersect at one point in a system of equations?

Back

It means there is exactly one solution to the system, which is the coordinates of the intersection point.

Front

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

Back

It means they are the same line, indicating infinitely many solutions to the system.