solve systems by graphing

Front

What is the solution to a system of equations when two lines intersect?

Back

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

Front

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

Back

If two lines are parallel, it means there is no solution to the system of equations, as the lines never intersect.

Front

What does it indicate if two lines overlap when graphed?

Back

If two lines overlap, it indicates that there are infinitely many solutions to the system of equations, as every point on the line is a solution.

Front

How can you determine the number of solutions in a system of equations by graphing?

Back

You can determine the number of solutions by observing the intersection points of the lines: no intersection means no solution, one intersection means one solution, and overlapping lines mean infinitely many solutions.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

The graph is a straight line with a slope of 2 and a y-intercept of 3.

Front

If a system of equations has one solution, what does that look like on a graph?

Back

It looks like two lines intersecting 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, representing the value of y when x is 0.

Front

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

You find the solution by graphing both equations and identifying the point where the two lines intersect.

Front

What is the equation of a line in slope-intercept form?

Back

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