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 set of values that satisfy all equations in the system.

Front

How can you determine if a system of equations has no solution?

Back

A system of equations has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Two lines are parallel if they have the same slope and will never intersect, indicating that there is no solution to the system.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by the equations. The point of intersection is the solution.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the solution to the system of equations 5x - 4y = -16 and x + 2y = -6?

Back

The solution is (-4, -1).

Front

What is the solution to the system of equations y = 4x + 1 and 3x + 2y = 13?

Back

The solution is (1, 5).

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you identify the slope of a line from an equation in slope-intercept form?

Back

In slope-intercept form (y = mx + b), 'm' represents the slope of the line.