On the grid show, by shading, the region that satisfies all of these inequalities - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 1
Question 18
On the grid show, by shading, the region that satisfies all of these inequalities.
$$2y + 4 < x$$
$$x < 3$$
$$y < 6 - 3x$$
Label the region R.
Worked Solution & Example Answer:On the grid show, by shading, the region that satisfies all of these inequalities - Edexcel - GCSE Maths - Question 18 - 2021 - Paper 1
Step 1
Draw the line for $2y + 4 < x$
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Answer
To rearrange the inequality:
2y<x−4y<21x−2
This line has a slope of 21 and a y-intercept at −2. Draw this line using a dashed line to indicate that the region above this line satisfies the inequality.
Step 2
Draw the line for $x < 3$
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Answer
This vertical line is drawn at x=3. Use a dashed line for this line as well, as it indicates that the region to the left of this line satisfies the inequality.
Step 3
Draw the line for $y < 6 - 3x$
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Answer
Rearranging gives:
y<6−3x
The line has a slope of −3 and a y-intercept of 6. Draw this line with a dashed line, shading the area below, as this represents the region where the inequality holds true.
Step 4
Label the region R
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Answer
Identify the area where all three shaded regions overlap. This is the region R. Ensure it is clearly marked on the graph.
