Solving Systems by Graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, which represents the values of the variables that satisfy both equations.

Front

What does it mean if two lines are parallel in a graph?

Back

Parallel lines never intersect because they have the same slopes.

Front

How can you determine the solution to a system of equations by graphing?

Back

By plotting both equations on the same graph and identifying the point where they intersect.

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 is zero.

Front

If two lines have different slopes, what can be said about their intersection?

Back

If two lines have different slopes, they will intersect at exactly one point.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines are parallel and never intersect.

Front

What is the graphical representation of the solution (4, -1)?

Back

The point (4, -1) is where the two lines intersect on the graph.

Front

What is the solution to the system of equations if the lines intersect at (4, -2)?

Back

The solution is (4, -2), which is the point of intersection.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it indicate if two lines have the same y-intercept?

Back

If two lines have the same y-intercept but different slopes, they will intersect at one point and are not parallel.