Systems

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 if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

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, the point is a solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection points of the lines corresponding to the equations.

Front

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

Back

(1, 3)

Front

What is the slope of the line represented by the equation y = mx + b?

Back

The slope is 'm', which indicates the steepness and direction of the line.

Front

What does it mean for two lines to be perpendicular?

Back

Their slopes are negative reciprocals of each other.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.