The diagram shows the graph of $x^2 + y^2 = 30.25$ - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 1
Question 21
The diagram shows the graph of $x^2 + y^2 = 30.25$.
Use the graph to find estimates for the solutions of the simultaneous equations
$x^2 + y^2 = 30.25$
y - 2x = 1
Worked Solution & Example Answer:The diagram shows the graph of $x^2 + y^2 = 30.25$ - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 1
Step 1
Plot the graph of $y - 2x = 1$
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Answer
First, rearrange the equation to find the points:
y=2x+1
This is a linear equation with a slope of 2. You can find points by setting values for x:
For x=0, y=1.
For x=1, y=3.
Plot these points on the graph.
Step 2
Find intersection points with the circle
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Answer
Look for where the line intersects the circle defined by x2+y2=30.25.
When plotting, estimate the intersection points to the nearest coordinates:
One intersection at approximately (5,6).
Another intersection at approximately (−6,−5).
These points represent the estimated solutions to the simultaneous equations.
