13 (a) On the grid show, by shading, the region that satisfies all these inequalities. $x \geq 0$ $x \leq 2$ $y \leq x + 3$ $2x + 3y \geq 6$ Label the region R. (b) The diagram below shows the region S that satisfies the inequalities $y \leq 4x$ $y \geq \frac{1}{2}x$ $x + y \leq 6$ Geoffrey says that the point with coordinates (2, 4) does not satisfy all the inequalities because it does not lie in the shaded region. Is Geoffrey correct? You must give a reason for your answer.

GCSE Edexcel Maths The Circle: 13 (a) On the grid show, by shad

13 (a) On the grid show, by shading, the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 3

Question 14

13 (a) On the grid show, by shading, the region that satisfies all these inequalities. $x \geq 0$ $x \leq 2$ $y \leq x + 3$ $2x + 3y \geq 6$ Label the region R. (... show full transcript

Worked Solution & Example Answer:13 (a) On the grid show, by shading, the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 3

Step 1

Show the region that satisfies all these inequalities.

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Answer

To find the region R defined by the inequalities, we need to graph each one:

Graph $x \geq 0$ : This represents the right side of the y-axis.
- Shade to the right of the y-axis.
Graph $x \leq 2$ : This is a vertical line at $x=2$ .
- Shade to the left of this line.
Graph $y \leq x + 3$ : This is a line with a y-intercept at $(0, 3)$ and a slope of 1.
- Draw the line and shade below it.
Graph $2x + 3y \geq 6$ : Rearranging gives $y \geq -\frac{2}{3}x + 2$ .
- Draw the line with a y-intercept at 2 and a slope of -2/3, and shade above this line.

The solution region R is where all shaded areas overlap, found within the bounded area of these lines.

Step 2

Is Geoffrey correct?

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Answer

To determine if Geoffrey is correct regarding the point (2, 4):

**Check $y \leq 4x** for (2, 4): Substituting,$ 4 \leq 4(2)$ which is true.
**Check $y \geq \frac{1}{2}x** for (2, 4): Substituting,$ 4 \geq \frac{1}{2}(2)$ which is also true.
**Check $x + y \leq 6** for (2, 4): Substituting,$ 2 + 4 \leq 6$, which is not true.

Thus, although (2, 4) satisfies the first two inequalities, it fails the third. Therefore, Geoffrey is correct.

13 (a) On the grid show, by shading, the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 3

Worked Solution & Example Answer:13 (a) On the grid show, by shading, the region that satisfies all these inequalities - Edexcel - GCSE Maths - Question 14 - 2020 - Paper 3

Show the region that satisfies all these inequalities.

Is Geoffrey correct?

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