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Answers
Step-by-step explanation:
2y + 5/2 = 37/2
2y = 16
y = 8
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Answer:
systems of three equations requires a bit more organization and a touch of visual gymnastics.
Solving Systems of Three Equations in Three Variables
In order to solve systems of equations in three variables, known as three-by-three systems, the primary tool we will be using is called Gaussian elimination, named after the prolific German mathematician Karl Friedrich Gauss. While there is no definitive order in which operations are to be performed, there are specific guidelines as to what type of moves can be made. We may number the equations to keep track of the steps we apply. The goal is to eliminate one variable at a time to achieve upper triangular form, the ideal form for a three-by-three system because it allows for straightforward back-substitution to find a solution \displaystyle \left(x,y,z\right),\text{}(x,y,z), which we call an ordered triple. A system in upper triangular form looks like the following:
A
x
+
B
y
+
C
z
=
D
E
y
+
F
z
=
G
H
z
=
K
The third equation can be solved for \displaystyle z,\text{}z, and then we back-substitute to find \displaystyle yy and \displaystyle xx. To write the system in upper triangular form, we can perform the following operations:
Interchange the order of any two equations.
Multiply both sides of an equation by a nonzero constant.
Add a nonzero multiple of one equation to another equation.
The solution set to a three-by-three system is an ordered triple \displaystyle \left\{\left(x,y,z\right)\right\}{(x,y,z)}. Graphically, the ordered triple defines the point that is the intersection of three planes in space. You can visualize such an intersection by imagining any corner in a rectangular room. A corner is defined by three planes: two adjoining walls and the floor (or ceiling). Any point where two walls and the floor meet represents the intersection of three planes.