On the grid show, by shading, the region that satisfies all of these inequalities - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 1
Question 17
On the grid show, by shading, the region that satisfies all of these inequalities.
$2y + 4 < x < 3$
$y < 6 - 3x$
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 17 - 2021 - Paper 1
Step 1
Sketch the line for $2y + 4 < x$
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Answer
To find the line represented by the equation 2y+4=x, we can rearrange it to express y in terms of x:
2y=x−4y=21x−2
This is a straight line with a slope of rac{1}{2} and a y-intercept at −2. We will draw this line on the graph making sure it is dashed to represent that points on the line are not included (due to the '<' symbol).
Step 2
Sketch the line for $x < 3$
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Answer
The vertical line at x=3 will also be dashed. This line divides the graph into two regions; we are interested in the region to the left of this line (not including the line itself).
Step 3
Sketch the line for $y < 6 - 3x$
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Answer
Rearranging the inequality y<6−3x, we can draw the boundary line given by y=6−3x. This line has a y-intercept of 6 and a slope of −3. Again, a dashed line will be drawn because the inequality is strict ('<').
Step 4
Shade the correct region R
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Answer
The region R is the area where all three inequalities overlap. This means we will shade the area that is to the left of the line x=3, above the line y=21x−2, and below the line y=6−3x. Make sure to clearly indicate this shaded region on the graph and label it R.
