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
: 1.4.7
Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.
Calculator Active?
No
Question
:
y
=
8
x
−
2
4
x
+
y
=−
14
What is the solution (
x , y
)
to the system of equations above?
A)
(−
1,10
)
B)
(
1,10
)
C)
(−
1
,
−
10
)
D)
(
0.5
,
−
10
)
Correct answer: C
Equation Upload
(Please write the text of the question along with the LaTeX Code):
$y=8x-2$
$4x+y=-14$
What is the solution $(x,y)$ to the system of equations above?
A) $( -1,10)$
B) $(1,10)$
C) $(-1,-10)$
D) $(0.5,-10)$
On a scale of 1-10, how difficult would you estimate your question to be (1=easy, 10=extremely difficult):
5 i
Solution
:
Step 1
: Plug the expression 8
x
−
2
in the second equation.
4
x
+
8
x
−
2
=−
14
12
x
−
2
+
2
=−
14
+
2
12
x
=−
12
12
x
12
=
−
12
12
x
=−
1
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 1}: Plug the expression $8x-2$ in the second equation.
$$4x+8x-2=-14$$
$$12x-2+2=-14+2$$
$$12x=-12$$
$$\frac{12x}{12}=\frac{-12}{12}$$
$$x=-1$$
Step 2:
Plug x
=−
1
in the 1st equation to solve for y
.
y
=
8
(−
1
)−
2
¿
−
8
−
2
¿
−
10
Correct solution is (
x , y
)=(−
1
,
−
10
)
Equation Upload (Please write the text of the question along with the LaTeX Code):
\textbf{Step 2}: Plug $x=-1$ in the 1st equation to solve for $y$.
$$y=8(-1)-2$$
$$=-8-2$$
$$=-10$$
Correct solution is $(
𝑥
,) = (−1,−10)$
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