(3) For the solution of an equation x + y = 14 choose the wrong
set of values of x and y.
(a) 8,6 (b) 7,4 (c) 7,5 (d) 12,2
Answers
Answer:
Step-by-step explanation:
A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.
LEARNING OBJECTIVES
Explain what systems of equations can represent
KEY TAKEAWAYS
Key Points
A system of linear equations consists of two or more linear equations made up of two or more variables, such that all equations in the system are considered simultaneously.
To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time.
In order for a linear system to have a unique solution, there must be at least as many equations as there are variables.
The solution to a system of linear equations in two variables is any ordered pair
(
x
,
y
)
that satisfies each equation independently. Graphically, solutions are points at which the lines intersect.
Key Terms
system of linear equations: A set of two or more equations made up of two or more variables that are considered simultaneously.
dependent system: A system of linear equations in which the two equations represent the
same line; there are an infinite number of solutions to a dependent system.
inconsistent system: A system of linear equations with no common solution because they
represent parallel lines, which have no point or line in common.
independent system: A system of linear equations with exactly one solution pair
(
x
,
y
)
.
A system of linear equations consists of two or more linear equations made up of two or more variables, such that all equations in the system are considered simultaneously. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all of the system’s equations at the same time. Some linear systems may not have a solution, while others may have an infinite number of solutions. In order for a linear system to have a unique solution, there must be at least as many equations as there are variables. Even so, this does not guarantee a unique solution.
In this section, we will focus primarily on systems of linear equations which consist of two equations that contain two different variables. For example, consider the following system of linear equations in two variables:
2
x
+
y
=
15
3
x
−
y
=
5
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4, 7) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations.
2
(
4
)
+
7
=
15
3
(
4
)
−
7
=
5
Both of these statements are true, so
(
4
,
7
)
is indeed a solution to the system of equations.
Note that a system of linear equations may contain more than two equations, and more than two variables. For example,
Answer:
( d ) 12,2
X + y = 14
X = 12 , y = 2
12+2=14