Thomas wanted to measure the width of the pond so he set up triangles as shown in the diagram. He claims the two triangles are s
imilar. How wide is the pond?
2 answers:
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Answer:
The ordered pair is indeed a solution to the system:
.
Step-by-step explanation:
Consider a system of equations about variables and
. An ordered pair
(where
and
are constant) is a solution to that system if and only if all equations in that system hold after substituting in
and
.
For the system in this question, would be a solution only if both equations in the system hold after replacing all
in equations of the system with
and all
with
.
The of the equation
would become
. The
of that equation would become
. The two sides are indeed equal.
Similarly, the of the equation
would become
. The
of that equation would become
. The two sides are indeed equal.
Thus, and
simultaneously satisfy both equations of the given system. Therefore, the ordered pair
would indeed be a solution to that system.