Graphing Linear Systems

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Graphing a system of equations involves plotting the equations on the same coordinate plane to find their point of intersection, which represents the solution.

The solution to a system of equations is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

If two lines are parallel, it means they have the same slope and will never intersect, indicating that the system has no solution.

If two lines coincide, they lie on top of each other and have infinitely many solutions, as every point on the line is a solution.

The slope of a line can be found from the equation in slope-intercept form (y = mx + b) where m represents the slope.

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

A system of equations has one solution if the lines intersect at exactly one point, meaning they have different slopes.

The graph of y = 2x + 1 is a straight line with a slope of 2 and a y-intercept at (0, 1).

To solve by graphing, plot each equation on the same coordinate plane and identify the point where they intersect.