MATH 140 -- Intermediate Algebra -- Exercise Solutions
Section: 4.1

DEFINITION: A solution of a system of linear equations is an ordered n-tuple of numbers which makes all of the equations true when the n-tuple of numbers is substituted into the equations.

1. Is the point (2, -1) the solution of the system
Answer: Substitute the coordinates of (2, -1) into the equations to obtain
Because the coordinates of the point (2, -1) satisfy both equations, the point is the solution of the system.
From this we know the two lines in the system intersect at the point (2, -1)

3. Is the point (3, 5) the solution of the system
Answer: Substitute the coordinates of (3, 5) into the equations to obtain
Because the coordinates of the point (3, 5) DO NOT satisfy the second equation the point (3, 5) is not a solution of the system.

15. Use the substitution method to solve the system
Give a graphical interpretation.
Answer:

The solutions of the system is the point (2, 8).

17. Use the substitution method to solve the system
Give a graphical interpretation.
Answer:

The solution of the system is the point (0,-9)

19. Use the substitution method to solve the system
Give a graphical interpretation.
Answer:

The solution of the system is the point (1, -1)

               

21. Use the substitution method to solve the system
Give a graphical interpretation.
Answer:

The solution of the system is the point (- 5, 3)

23. Use the elimination method to solve the system
Give a graphical interpretation.
Answer:

25. Use the elimination method to solve the system
Give a graphical interpretation.
Answer:

The solution is the point (1, -2)

Observe that this alternate solution BELOW is probably a more efficient and easier set of steps for solving the above system.
Future systems will be solved in this manner to reduce the number of steps and to make the work easier.

27. Use the elimination method to solve the system
Give a graphical interpretation.
Answer:

The solution to the system is the point (9, 9)
Notice that nothing worked out nicely in this problem--no shortcuts.

31. Use the elimination method to solve the system
Give a graphical interpretation.
Answer:

The false statement in row two indicates there is no solution.
Rewrite the two equation in slope intercept form to see clearly why there is no solution

Clearly the two lines are parallel and do not intersect. Their graphs also seem to indicate that they are parallel lines.

37. Use the elimination method to solve the system
Give a graphical interpretation.
Answer: