Solving pairs of linear equations in two variables

Front

What is a linear equation in two variables?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

Front

What is the y-intercept of a line?

Back

Front

What does it mean for two lines to be parallel?

Back

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

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.

Front

How can you determine if a point (x, y) is a solution to a system of equations?

Back

A point (x, y) is a solution to a system of equations if it satisfies all equations in the system when substituted for x and y.

Front

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

Back

The graphical method involves plotting both equations on a graph and identifying the point of intersection, which represents the solution.

Front

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

Back

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

Front

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

Back

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