Understanding Solutions to Systems of Equations

The video tutorial explains how to determine if an ordered pair is a solution to a system of equations. It involves substituting the pair into each equation to check if both are satisfied. The tutorial also demonstrates a graphical method to verify the solution by plotting the equations and identifying the intersection point. The ordered pair is confirmed as a solution both algebraically and graphically.

What is the first step in determining if an ordered pair is a solution to a system of equations?

• Solve for x and y

• Graph the equations

• Check if the equations are linear

• Substitute the values into the equations

What is the result of substituting x = -6 and y = -1 into the first equation 3x + y = -19?

• -20

• -19

• -18

• -17

Why does satisfying the first equation not guarantee that the ordered pair is a solution to the system?

• Because the ordered pair might be incorrect

• Because the ordered pair must satisfy both equations

• Because the equations might be inconsistent

• Because the system might have no solutions

What is the result of substituting x = -6 and y = -1 into the second equation 4x + 3y = -27?

• -26

• -25

• -27

• -28

What conclusion can be drawn if an ordered pair satisfies both equations in a system?

• The system is inconsistent

• The ordered pair is incorrect

• The ordered pair is a solution to the system

• The system has no solution

What is the purpose of graphically verifying the solution to a system of equations?

• To find the slope of the lines

• To check if the ordered pair is the intersection point

• To determine if the lines are parallel

• To calculate the y-intercept

What does the intersection point of two lines on a graph represent in terms of a system of equations?

• The point where the lines are parallel

• The solution to the system of equations

• The midpoint of the lines

• The point where the lines are perpendicular

If an ordered pair is on both lines of a system of equations, what does this indicate?

• The system has no solution

• The ordered pair is a solution to the system

• The ordered pair is not a solution

• The lines are parallel

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

• The point where the lines intersect

• The point where the lines are parallel

• The point where the lines are perpendicular

• The midpoint of the lines

What is the significance of verifying a solution both algebraically and graphically?

• It confirms the solution is correct

• It shows the equations are inconsistent

• It proves the lines are parallel

• It demonstrates the system has no solution