Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

What does it mean for two lines to be parallel in a linear system?

Back

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

Front

What is the solution of a linear system with intersecting lines?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

What is the solution of a linear system with coincident lines?

Back

The solution is infinitely many solutions, as every point on the line satisfies both equations.

Front

How do you determine if a linear system has no solution?

Back

A linear system has no solution if the lines are parallel, meaning they do not intersect.

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

How do you convert the equation 3x - 6y > 12 into slope-intercept form?

Back

y < (1/2)x - 2.

Front

What does it mean if a linear system has one solution?

Back

It means the lines intersect at exactly one point, providing a unique solution for the variables.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

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, indicating the value of y when x = 0.