6.1 Practice: Graphing Systems of Linear Equations

Front

What is the solution to the system of equations?

Back

The solution is the point where the two lines intersect. For example, for the equations y = 2x + 1 and y = -x + 3, the solution is (1, 3).

Front

How many solutions can a system of linear equations have?

Back

A system of linear equations can have one solution, no solution, or infinitely many solutions.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, it means they have no points in common, resulting in no solution for the system.

Front

What does it mean if two lines are the same in a system of equations?

Back

If two lines are the same, it means they overlap completely, resulting in infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines representing the equations.

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 determine if a system of equations has one solution?

Back

A system has one solution if the lines intersect at exactly one point.

Front

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

Back

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

Front

How can you tell if two lines are intersecting?

Back

Two lines are intersecting if they have different slopes and meet at a single point.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.