System of Equations

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations in the system true.

Front

What is the graphical representation of a system of equations?

Back

The graphs of the equations, where the point of intersection represents the solution.

Front

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

Back

The system has no solution because the lines never intersect.

Front

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

Back

The system has infinitely many solutions because the lines are the same.

Front

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

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

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

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

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

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the importance of the slope in a system of equations?

Back

The slope indicates the steepness of the line; lines with the same slope are parallel.

Front

What is the y-intercept in the context of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.