solve system 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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it indicate if two lines are parallel when graphing a system of equations?

Back

The system has no solution because the lines never intersect.

Front

What does it indicate if two lines coincide when graphing a system of equations?

Back

The system has infinitely many solutions because the lines are the same.

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: intersecting lines have one solution, parallel lines have no solutions, and coinciding lines have infinitely many solutions.

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

Back

Set x = 0 in the equation and solve for y.

Front

What is the slope of the line represented by the equation y = 1/2x + 2?

Back

1/2, which means for every 1 unit increase in x, y increases by 1/2 unit.

Front

What is the y-intercept of the equation y = -3x + 9?

Back

9, which is the point where the line crosses the y-axis.