Solving Systems by Graphing

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by graphing?

Back

Solving a system of equations by graphing involves plotting the equations on a coordinate plane and identifying the point(s) where the graphs intersect.

Front

What is the graphical representation of the equation 2x + 2y = 6?

Back

To graph the equation 2x + 2y = 6, first rewrite it in slope-intercept form (y = -x + 3) and then plot the line using the y-intercept and slope.

Front

How do you find the y-intercept of a linear equation?

Back

The y-intercept of a linear equation is found by setting x = 0 and solving for y.

Front

What is the slope of the line represented by the equation y = -x + 3?

Back

The slope of the line y = -x + 3 is -1.

Front

What does the solution (1, -1) represent in the context of a system of equations?

Back

The solution (1, -1) represents the point where the two equations in the system intersect, indicating that x = 1 and y = -1 satisfy both equations.

Front

What is the significance of the point (3, 3) in a system of equations?

Back

The point (3, 3) is the solution to the system of equations, meaning it is the point where the graphs of the equations intersect.

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What is the method to check if a point is a solution to a system of equations?

Back

To check if a point is a solution, substitute the x and y values of the point into each equation. If both equations are satisfied, the point is a solution.

Front

What does it mean if two lines intersect at a single point?

Back

If two lines intersect at a single point, it means the system of equations has a unique solution.