Systems of Equations - Graphing Guided Notes

What defines a system of equations?

• A set of equations with different variables

• A single equation with one variable

• Two or more equations sharing the same variables

• A mathematical expression without variables

What is the result of a system of equations with different slopes?

• No solution

• Exactly one solution

• Infinite solutions

• Cannot be determined

How do you graph a line given its slope and y-intercept?

• Plot the y-intercept and use the slope to find another point

• Plot the slope on the x-axis

• Use the slope as the y-intercept

• Graph only the y-intercept

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

• Finding the intersection point of the lines

• Graphing only one equation

• Ensuring the slopes are different

• By checking if the y-intercept matches

In the context of systems of equations, what does 'consistent and independent' mean?

• The system has no solution

• The system has infinite solutions

• The equations are unrelated

• The system has exactly one solution

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

• They intersect at one point

• They will never intersect

• They overlap completely

• They intersect at multiple points

What indicates a system of equations has infinite solutions?

• Each equation has a different slope

• The equations represent the same line

• The lines intersect at multiple points

• The equations form parallel lines

What is the solution to a system of equations that do not intersect?

• Two solutions

• Infinite solutions

• No solution

• One solution

What does a 'consistent and dependent' system indicate?

• The system has no solution

• The system has exactly one solution

• The system has infinite solutions

• The equations are inconsistent

What method involves graphing lines to find the solution of a system of equations?

• Elimination method

• Substitution method

• Matrix method

• Graphing method