On the grid, shade the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 2
Question 14
On the grid, shade the region that satisfies all these inequalities.
$y > 1$
$x + y < 5$
$y > 2x$
Label the region $R$.
(Total for Question 14 is 3 marks)
Worked Solution & Example Answer:On the grid, shade the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2017 - Paper 2
Step 1
Plot the line $y = 1$
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Answer
To start, draw a horizontal line at y=1. This line is not included in the solution since the inequality is y>1, so use a dashed line to represent it.
Step 2
Plot the line $x + y = 5$
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Answer
Rearranging this equation gives y=5−x. Draw a dashed line that passes through the points (0,5) and (5,0), since this line is also not included in the solution (x+y<5).
Step 3
Plot the line $y = 2x$
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Answer
This line is represented by the equation y=2x. Draw a dashed line through the origin (0,0), extending upwards to the right, as for the inequality y>2x; this line is also not included in the solution.
Step 4
Shade the region $R$
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Answer
The feasible region R is the area that satisfies all inequalities: above the line y=1, below the line y=5−x, and above the line y=2x. Shade the intersection of these areas and label it R.
