Linear Equations and Systems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What does it mean to solve a system of linear equations?

Back

To solve a system of linear equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method in solving linear equations?

Back

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

Front

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

Back

A point is a solution to a system of equations if it satisfies all equations in the system when the coordinates of the point are substituted into the equations.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

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 graph a linear equation?

Back

To graph a linear equation, you can find two or more points that satisfy the equation and plot them on a coordinate plane, then draw a line through these points.

Front

What is a consistent system of equations?

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.