Solving System of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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, which represents the solution(s) to the system.

Front

What is the solution to a system of equations?

Back

The values of the variables that satisfy all equations in the system simultaneously.

Front

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

Back

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

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

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

Back

It means there are infinitely many solutions, as the lines overlap completely.

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

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 between two points.

Front

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

Back

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

Front

What is the significance of the intersection point of two lines?

Back

It represents the solution to the system of equations, indicating where both equations are true.