Systems of Equations 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 a solution?

Back

A solution is a set of values for the variables that makes all equations true.

Front

How can you find the solution to a system of equations graphically?

Back

By graphing the equations and identifying the point(s) where the lines intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, meaning there is no solution.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

One solution: lines intersect at one point; No solution: lines are parallel; Infinitely many solutions: lines are the same.

Front

What is the graphical representation of the equation y = 2x + 3?

Back

A straight line with a slope of 2 and a y-intercept of 3.

Front

What does it mean for two lines to be coincident?

Back

They lie on top of each other, representing the same line and thus have infinitely many solutions.

Front

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

Back

Substitute the point's coordinates into each equation; if they satisfy all equations, it is a solution.