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 one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

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 does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (if ≤ or ≥) or dashed line (if < or >). 2. Shade the region that satisfies the inequality.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the solution to a system of equations graphically?

Back

Plot both equations on the same graph and identify the point(s) where they intersect.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is a linear inequality?

Back

An inequality that involves a linear expression, such as y < 2x + 3.