MAT 101 AUGMENTED MATRICES TOPIC 14
EXAM 4 2026 COMPLETE PROBLEM SET
QUESTIONS AND CORRECT ANSWERS FULL
REVIEW
◉ *System of Linear Equations*. Answer: When two or more linear
equations are grouped together, they form a system of linear
equations.
◉ Solutions to a System of Equations. Answer: The solutions of a
system of equations are the values of the variables that make *all*
the equations true.
A solution of a system of two linear equations is represented by an
ordered pair (x, y)
◉ HOW TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY
*GRAPHING*:. Answer: (1) Graph the first equation.
(2) Graph the second equation on the same rectangular coordinate
system.
(3) Determine whether the lines intersect, are parallel, or are the
same line.
(4) Identify the solution to the system.
If the lines intersect, identify the point of
,intersection. This is the solution to the
system.
If the lines are parallel, the system has no
solution.
If the lines are the same, the system has
an infinite number of solutions.
(5) Check the solution in both equations.
◉ *Coincident Lines*. Answer: Two lines or shapes that lie exactly
on top of each other. Coincident lines have the *same slope and same
y-intercept*.
◉ *consistent system of equations*. Answer: A consistent system of
equations is a system of equations with at least one solution
◉ *inconsistent system of equations*. Answer:
◉ Identify which of the following systems is consistent and which
ones are inconsistent system
(1) A system of linear equations whose graphs(lines) *intersect*. For
example:
3x + y = − 1
2x + y = 0
, (2) A system of linear equations whose graphs(lines) are *parallel*
lines. For example:
y = 1/2x − 3
x − 2y = 4
.
(3) A system of linear equations whose graphs(lines) are
*coincident* lines. For example:
y = 2x − 3
−6x + 3y = − 9.. Answer: (1) Since the system has graphs that
intersect, then it's a consistent system, because it has *one* solution.
(2) Since the system is with parallel lines, then it's an inconsistent
system, because it has *no* solution.
(3) Since the system is with coincident lines, then it's consistent
system, because it has *infinitely many* solution.
◉ We also categorize the equations in a system of equations by
calling the equations *independent* or *dependent*. What is the
difference between independent equations and dependent
equations?. Answer: If two equations are independent, they each
have their own set of solutions. Intersecting lines and parallel lines
are independent.
EXAM 4 2026 COMPLETE PROBLEM SET
QUESTIONS AND CORRECT ANSWERS FULL
REVIEW
◉ *System of Linear Equations*. Answer: When two or more linear
equations are grouped together, they form a system of linear
equations.
◉ Solutions to a System of Equations. Answer: The solutions of a
system of equations are the values of the variables that make *all*
the equations true.
A solution of a system of two linear equations is represented by an
ordered pair (x, y)
◉ HOW TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY
*GRAPHING*:. Answer: (1) Graph the first equation.
(2) Graph the second equation on the same rectangular coordinate
system.
(3) Determine whether the lines intersect, are parallel, or are the
same line.
(4) Identify the solution to the system.
If the lines intersect, identify the point of
,intersection. This is the solution to the
system.
If the lines are parallel, the system has no
solution.
If the lines are the same, the system has
an infinite number of solutions.
(5) Check the solution in both equations.
◉ *Coincident Lines*. Answer: Two lines or shapes that lie exactly
on top of each other. Coincident lines have the *same slope and same
y-intercept*.
◉ *consistent system of equations*. Answer: A consistent system of
equations is a system of equations with at least one solution
◉ *inconsistent system of equations*. Answer:
◉ Identify which of the following systems is consistent and which
ones are inconsistent system
(1) A system of linear equations whose graphs(lines) *intersect*. For
example:
3x + y = − 1
2x + y = 0
, (2) A system of linear equations whose graphs(lines) are *parallel*
lines. For example:
y = 1/2x − 3
x − 2y = 4
.
(3) A system of linear equations whose graphs(lines) are
*coincident* lines. For example:
y = 2x − 3
−6x + 3y = − 9.. Answer: (1) Since the system has graphs that
intersect, then it's a consistent system, because it has *one* solution.
(2) Since the system is with parallel lines, then it's an inconsistent
system, because it has *no* solution.
(3) Since the system is with coincident lines, then it's consistent
system, because it has *infinitely many* solution.
◉ We also categorize the equations in a system of equations by
calling the equations *independent* or *dependent*. What is the
difference between independent equations and dependent
equations?. Answer: If two equations are independent, they each
have their own set of solutions. Intersecting lines and parallel lines
are independent.
