Solving Systems of Linear Equations in Two Variables

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 if a system has one solution?

Back

The lines intersect at exactly one point, representing a unique solution.

Front

What does it mean if a system has no solution?

Back

The lines are parallel and never intersect.

Front

What does it mean if a system has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable.

Front

How do you solve a system by substitution?

Back

Solve one equation for one variable and substitute it into the other equation.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

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 intersection of two lines graphically?

Back

Locate the point where the two lines cross on the graph.

Front

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

Back

They determine the slope and position of the line.