Systems of eq and ineq REVIEW

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 if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

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

Back

By graphing the equations and observing the intersection points: one solution (intersecting), no solution (parallel), or infinitely many solutions (same line).

Front

What is the elimination method in solving systems of equations?

Back

A method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

A method where you solve one equation for one variable and substitute that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

A method where you graph both equations on the same coordinate plane and find the point(s) of intersection.

Front

What is the significance of the x-axis and y-axis in a coordinate plane?

Back

The x-axis is the horizontal line, and the y-axis is the vertical line; they intersect at the origin (0,0).

Front

What are the four quadrants in a coordinate plane?

Back

Quadrant I (x>0, y>0), Quadrant II (x<0, y>0), Quadrant III (x<0, y<0), Quadrant IV (x>0, y<0).

Front

How do you identify the coordinates of a point on the graph?

Back

The coordinates are given as (x, y), where x is the horizontal distance from the origin and y is the vertical distance.