Systems of Linear Equations and Inequalities Review

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the boundary line, indicating all the solutions that satisfy the inequality.

Front

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

Back

Substitute the point's coordinates into each equation. If all equations are satisfied, the point is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to intersect?

Back

It means they have exactly one solution, which is the point where they cross.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

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

Back

The area on a graph where all the constraints of the inequalities are satisfied.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows a straight line, while a linear inequality shows a region of solutions.