Linear equations in two variables.

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by + c = 0, where a, b, and c are constants, and x and y are variables.

Front

What does it mean for a system of equations to have a unique solution?

Back

A system of equations has a unique solution if the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution if the graphs of the equations are parallel lines, meaning they never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions if the graphs of the equations coincide, meaning they are the same line.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

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

Front

What is the graphical representation of the equation 2x + 3y - 6 = 0?

Back

The graphical representation is a straight line in the Cartesian plane.

Front

How do you find the intersection point of two lines given by their equations?

Back

To find the intersection point, solve the system of equations simultaneously using substitution or elimination methods.

Front

What is the significance of the determinant in a system of linear equations?

Back

The determinant helps determine the nature of the solutions: if it's non-zero, the system has a unique solution; if it's zero, the system may have no or infinitely many solutions.

Front

What is the condition for two lines to be perpendicular?

Back

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