Solving Systems of Equations Graphically

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solution?

Back

It means the graphs of the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means the graphs of the equations coincide, representing the same line.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and connecting them with a straight line.

Front

What is the solution to the system of equations represented graphically?

Back

The point where the graphs of the equations intersect.

Front

What is the ordered pair solution of the system: y = 2x + 1 and y = -x + 4?

Back

(1, 3)

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if both equations are true, it is a solution.

Front

What is the significance of the x-intercept in a graph of a linear equation?

Back

The x-intercept is the point where the graph crosses the x-axis, indicating the value of x when y = 0.

Front

What is the significance of the y-intercept in a graph of a linear equation?

Back

The y-intercept is the point where the graph crosses the y-axis, indicating the value of y when x = 0.