Solving Systems of Linear Equations by Graphing

This video tutorial covers solving systems of linear equations by graphing. It explains the three types of solutions: unique, no solution, and infinitely many solutions. The tutorial includes examples of verifying solutions and solving systems in both slope-intercept and standard forms, with graphical and calculator verification.

What is a system of linear equations?

• Two equations with different variables

• Two equations with the same variables

• One equation with two variables

• Two equations with no variables

What does it mean if two lines intersect at exactly one point?

• The system is inconsistent

• There is no solution

• There are infinitely many solutions

• There is one unique solution

What is the term for a system of equations with no solutions?

• Consistent

• Inconsistent

• Dependent

• Independent

How do you verify if an ordered pair is a solution to a system of equations?

• By solving the equations algebraically

• By substituting the values into both equations

• By using a calculator

• By graphing the equations

What is the slope-intercept form of a linear equation?

• x = my + b

• ax + by = c

• y = ax + b

• y = mx + b

What is the vertical intercept of the equation y = x + 1?

• (1, 1)

• (0, 1)

• (1, 0)

• (0, 0)

How do you graph the equation y = 4/3x + 6?

• Plot the intercept and use the slope to find other points

• Solve for x and y

• Use a graphing calculator

• Plot random points

What is the solution to the system of equations if the lines intersect at (-3, 2)?

• (-3, 2)

• (2, -3)

• (3, -2)

• (-2, 3)

What is the first step in solving 4x - 3y = -18 for y?

• Divide by -3

• Subtract 4x from both sides

• Multiply by -3

• Add 4x to both sides

How do you find the point of intersection using a graphing calculator?

• Press 'Graph' and look for the intersection

• Use the 'Zoom' function

• Press '2nd' then 'Trace' and select 'Intersection'

• Enter the equations and solve manually