Systems of Linear Equations and Inequalities Review

Front

What is a system of linear equations?

Back

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

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

A system has one solution if the lines intersect at a single point, no solution if the lines are parallel, and infinitely many solutions if the lines coincide.

Front

What is the graphical representation of a linear inequality?

Back

A linear inequality is represented by a shaded region on one side of the line, indicating all the solutions that satisfy the inequality.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for a system of inequalities to be consistent?

Back

A consistent system of inequalities has at least one solution that satisfies all inequalities.

Front

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

Back

A linear equation shows a relationship that is equal, while a linear inequality shows a relationship that is not necessarily equal, allowing for a range of solutions.

Front

How can you represent a system of inequalities graphically?

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

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 x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.