Systems of Equations Flashcard

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 point(s) where the equations intersect.

Front

What does it mean for two lines to be parallel in terms of slope?

Back

Two lines are parallel if they have the same slope. This means they will never intersect.

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

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 other variable.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solution, meaning the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to be dependent?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the first step in solving the system of equations 2x + 3y = 6 and 4x + 6y = 12 using elimination?

Back

You can multiply the first equation by 2 to align the coefficients of x or y for elimination.