Week 16 (12.06.24) Review Systems of Equations

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

It means there is at least one set of values for the variables that satisfies all equations in the system.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

What are parallel lines in the context of systems of equations?

Back

Lines that never intersect and have the same slope.

Front

What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that do not intersect.

Front

What is the solution to the system of equations: y = 2x + 1 and y = 2x - 3?

Back

No solution, as the lines are parallel.

Front

What is the solution to the system of equations: y = x + 2 and y = -x + 4?

Back

(1, 3), where the lines intersect.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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