SME
Grade 9 Math · Problem type
A box of points: a ≤ x ≤ b and c ≤ y ≤ d
Use this for “Shade the points with −3 ≤ x ≤ 2 and −1 ≤ y ≤ 4.”
Chart
Where all 4 shadings overlap, all 4 inequalities are true: those points are the solutions.
All the lines are solid: points on them are included.
Test (1, 2)
2 ≥ −1, 2 ≤ 4, 1 ≥ −3 and 1 ≤ 2: all true
It is a solution.
This is an example. Type your own values to start a new problem.
a
≤
x
≤
b
c
≤
y
≤
d
x₀
Test point x
example
y₀
Test point y
example
h
Is the test true?
worked out (not typed)
Formulas
test
(
x₀
,
y₀
)
in
a
≤
x
≤
b
and
c
≤
y
≤
d
:
h
test (1, 2) in −3 ≤ x ≤ 2 and −1 ≤ y ≤ 4: true
Assumptions
•
a ≤ x ≤ b is the strip between two upright lines, x = a and x = b.
•
c ≤ y ≤ d is the strip between two flat lines, y = c and y = d.
•
Where the strips overlap is a box: every point in it makes all four true.
Step-by-step
WE KNOW
a = −3, b = 2, c = −1, d = 4, x₀ = 1, y₀ = 2
FIND
is the test true? (h)
Step 1 · Find is the test true? (h)
Use test (x₀, y₀) in a ≤ x ≤ b and c ≤ y ≤ d: h
Check
x₀
between
a
and
b
,
and
y₀
between
c
and
d
:
true
when
all
four
are.
−3 ≤ 1 ≤ 2 is true
−1 ≤ 2 ≤ 4 is true
h
=
true
Check
Put the numbers back in. Both sides should match.
(1, 2) is in the box, so it is a solution ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Systems by elimination, and systems of linear inequalities
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