Solving 2 Variable Systems Graphically

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 to the system is the point(s) where the graphs of the equations intersect.

Front

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

Back

A system of equations has a unique solution when 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

A system of equations has no solution when 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

A system of equations has infinitely many solutions when the graphs of the equations are identical, meaning they represent the same line.

Front

How can you determine the solution of a system of equations graphically?

Back

To determine the solution graphically, plot the equations on a coordinate plane and identify the point(s) where the graphs intersect.

Front

What is the graphical representation of the equation y = mx + b?

Back

The equation y = mx + b represents a straight line on a graph, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

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What is the y-intercept of a line?

Back

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

Front

How do you find the intersection point of two lines graphically?

Back

To find the intersection point of two lines graphically, plot both lines on the same coordinate plane and look for the point where they cross.

Front

What is the significance of the solution (1, -1) in a system of equations?

Back

The solution (1, -1) indicates that when x = 1 and y = -1, both equations in the system are satisfied.