Solving Systems by Graphing Warmup

Front

What is the solution to the system of equations represented by the intersection of their graphs?

Back

The solution is the point where the graphs intersect, representing the values of x and y that satisfy both equations.

Front

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

Back

It means that the lines representing the equations are parallel and never intersect.

Front

What is the first step in solving a system of equations by graphing?

Back

Write both linear equations in slope-intercept form (y = mx + b).

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

What is slope-intercept form?

Back

Front

How can you convert an equation from standard form to slope-intercept form?

Back

Front

What does the slope of a line represent in a graph?

Back

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

Front

What is the y-intercept of a line?

Back

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

Front

If two lines have the same slope but different y-intercepts, what can be said about their solutions?

Back

The lines are parallel and have no solutions.

Front

What is the graphical representation of a system of equations?

Back

It is the plot of the equations on a coordinate plane, where the solutions are the points of intersection.