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
$$x^2 + y^2 = 30.25$$
$$y - 2x = 1$$ - 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
$$x^2 + y^2 = 30.25$$
$... show full transcript
Worked Solution & Example Answer: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
$$x^2 + y^2 = 30.25$$
$$y - 2x = 1$$ - Edexcel - GCSE Maths - Question 21 - 2021 - Paper 1
Step 1
Graph the equation $y - 2x = 1$
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Answer
To find where the line intersects the circle, we rearrange the linear equation to get
y=2x+1.
This line should be plotted on the same graph as the circle given by the equation x2+y2=30.25. The line will have a slope of 2 and a y-intercept of 1.
Step 2
Estimate the points of intersection
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Answer
By visually inspecting the graph, we find 2 points where the line intersects the circle. Estimations based on the graph suggest the following coordinates:
First Intersection: Approximately (2, 5)
Second Intersection: Approximately (-5, -7)
Providing both points as solutions will allow us to validate the answers.
