Linear Systems Review Extra credit 12/10

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 a system of equations to have no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

The equations represent the same line, meaning they overlap completely.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5)

Front

What does it mean for two lines to be skew?

Back

Skew lines are lines that do not intersect and are not parallel, existing in different planes.

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 find the intersection point of two lines?

Back

Set the equations equal to each other and solve for x, then substitute back to find y.

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.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on a graph where all the inequalities overlap, representing all possible solutions.