Solving Systems by Graphing

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 no solution?

Back

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

Front

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

Back

By finding the point(s) where the graphs of the equations intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning they overlap each other.

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify the slope of a line from its equation?

Back

The slope is the coefficient of x in the slope-intercept form.

Front

What is the y-intercept of a line?

Back

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

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

How do you graph the equation y + 9 = -3x?

Back

Rearrange to slope-intercept form: y = -3x - 9, then plot the y-intercept and use the slope to find another point.

Front

What does it mean for two lines to be perpendicular?

Back

Their slopes are negative reciprocals of each other.