Solving Linear Systems

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

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

Back

A unique solution means that 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

No solution means that the lines represented by the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

Infinite solutions occur when the equations represent the same line, meaning they coincide.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation. If both equations are true, the point is a solution.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

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 intersection point of two lines?

Back

To find the intersection point, solve the system of equations simultaneously.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the point where the line crosses the y-axis.

Front

What does the term 'slope' refer to in a linear equation?

Back

Slope refers to the steepness of the line, calculated as the rise over run (change in y over change in x).