Systems of Linear Equations and Inequalities

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

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

Front

What is the graphical representation of a system of equations with no solution?

Back

The lines are parallel and never intersect.

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

(3, 0)

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 there are countless points of intersection.

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, it is a solution.

Front

What is a linear inequality?

Back

An inequality that involves a linear expression, such as x + 2y < 5.

Front

How do you graph a linear inequality?

Back

Graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means not including the boundary, while '≥' includes the boundary.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3)