Identifying Solutions to Systems of Equations

Front

What is the solution to the system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

What does it mean if two lines are parallel?

Back

Parallel lines never intersect because they have the same slopes.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative).

Front

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

Back

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

Front

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

Back

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

Front

What is the y-intercept of a line?

Back

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

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point of intersection.

Front

What is the difference between one solution and no solution in a system of equations?

Back

One solution means the lines intersect at a single point; no solution means the lines are parallel.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed.

Front

What does it mean for two lines to have the same slope?

Back

It means they rise and run at the same rate, indicating they are parallel.