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 expressed in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

What does it mean for two lines to be parallel in the context of linear equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What is the condition for two linear equations to have infinitely many solutions?

Back

Two linear equations have infinitely many solutions if they represent the same line, meaning they are coincident.

Front

What does it mean for two lines to intersect at a point?

Back

Two lines intersect at a point if they have different slopes, resulting in a unique solution where they cross each other.

Front

What is the graphical representation of the equation x = a?

Back

The equation x = a represents a vertical line on the graph that crosses the x-axis at the point (a, 0).

Front

What is the graphical representation of the equation y = b?

Back

The equation y = b represents a horizontal line on the graph that crosses the y-axis at the point (0, b).

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the direction of the line when graphed.

Front

How can you determine if two lines are coincident?

Back

Two lines are coincident if their equations can be transformed into each other by multiplying or dividing by a non-zero constant.

Front

What is the unique solution of a system of linear equations?

Back

A unique solution occurs when the two lines intersect at exactly one point, indicating that the equations represent different lines.

Front

What does it mean if a system of linear equations has no solution?

Back

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