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Let’s check out your problem:
Is
(
1
,
9
)
(1,\,9)
(
1
,
9
)
a solution to this system of inequalities?
\newline
y
≤
x
+
10
y \leq x + 10
y
≤
x
+
10
\newline
y
≤
6
x
+
3
y \leq 6x + 3
y
≤
6
x
+
3
\newline
Choices:
\newline
(A)yes
\newline
(B)no
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Math Problems
Algebra 2
Is (x, y) a solution to the system of inequalities?
Full solution
Q.
Is
(
1
,
9
)
(1,\,9)
(
1
,
9
)
a solution to this system of inequalities?
\newline
y
≤
x
+
10
y \leq x + 10
y
≤
x
+
10
\newline
y
≤
6
x
+
3
y \leq 6x + 3
y
≤
6
x
+
3
\newline
Choices:
\newline
(A)yes
\newline
(B)no
Check Inequality
1
1
1
:
Check if
(
1
,
9
)
(1, 9)
(
1
,
9
)
satisfies the first inequality
y
≤
x
+
10
y \leq x + 10
y
≤
x
+
10
. Substitute
x
=
1
x = 1
x
=
1
and
y
=
9
y = 9
y
=
9
.
9
≤
1
+
10
9 \leq 1 + 10
9
≤
1
+
10
9
≤
11
9 \leq 11
9
≤
11
Check Inequality
2
2
2
:
Check if
(
1
,
9
)
(1, 9)
(
1
,
9
)
satisfies the second inequality
y
≤
6
x
+
3
y \leq 6x + 3
y
≤
6
x
+
3
.
\newline
Substitute
x
=
1
x = 1
x
=
1
and
y
=
9
y = 9
y
=
9
.
\newline
9
≤
6
×
1
+
3
9 \leq 6 \times 1 + 3
9
≤
6
×
1
+
3
\newline
9
≤
6
+
3
9 \leq 6 + 3
9
≤
6
+
3
\newline
9
≤
9
9 \leq 9
9
≤
9
Solution Verification:
Since
(
1
,
9
)
(1, 9)
(
1
,
9
)
satisfies both inequalities, it is a solution to the system.
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\newline
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(
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\newline
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x
+
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y
>
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7
x
+
9
y
>
−
3
?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
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Question
Is
(
−
4
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(
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4
,
−
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\newline
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