Systems of linear equations

Front

What is a system of linear equations?

Back

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

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What does it mean if a system of linear equations has one solution?

Back

The two lines represented by the equations intersect at exactly one point.

Front

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

Back

The two lines represented by the equations coincide, meaning they are the same line.

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation consists of lines on a coordinate plane.

Front

How can you determine if a system of linear equations has no solution?

Back

If the lines are parallel, they will never intersect, indicating no solution.

Front

What is the substitution method in solving systems of linear 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 linear equations?

Back

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

Front

What is the point of intersection in a system of linear equations?

Back

The point where the two lines intersect, representing the solution to the system.

Front

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

Back

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

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How do you find the slope of a line given two points?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1).