1.4
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School
University of California, Berkeley *
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Course
N54
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
3
Uploaded by BailiffBookElephant2276
Question and Solution Template
Learning Attribute(s) Included in Question
: 1.4.6 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system
with the same solutions.
Calculator Active?
No
Question
:
System A
: −
4
x
−
6
y
=
9
3
x
+
y
=−
4
System : −
4
x
−
6
y
=
9
−
x
−
5
y
=
5
How can we get System B
from System A
?
A)
Replace only the left-hand side of one equation with the
sum/difference of the left-hand sides of both equations
B)
Replace one equation with the sum/difference of both equations
C)
Swap only the right-hand sides of both equations
D)
Swap the order of the equations
Correct answer: B
Equation Upload
(Please write the text of the question along with the LaTeX Code):
System A: $-4x -6y=9$
$3x+y=-4$
System B : $-4x -6y=9$
$-x-5y=5$
How can we get System B from System A?
A) Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations
B) Replace one equation with the sum/difference of both equations
C) Swap only the right-hand sides of both equations
D) Swap the order of the equations
On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult):
4 i
Solution
:
Step 1
: Sum the equations in System A.
−
x
−
5
y
=
5
Replacing the second equation in System A
with this new equation, we
get a system that's equivalent to System A
:
−
4
x
−
6
y
=
9
−
x
−
5
y
=
5
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 1}: Sum the equations in System $A$.
$-x-5y=5$
Replacing the second equation in System $A$ with this new equation, giving a system that's equivalent to System $A$:
$-4x -6y=9$
$ -x-5y=5$
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