1. Solve Simultaneous Equations One Linear, one quadratic [Circle]
GCSE Higher

2. Content Equation of a circle Equation of straight line
Graphical Solution
Algebraic Solution [Substitution Method]

3. Equation of a Circle Is x2 + y2 = r2 Where The circle has centre (0,0)
Its radius is r

4. Consider x2 + y2 = 9 4 3 When y = 0, When x = 0, 2 x x2 = 9 y2 = 9 1-1 -2 -3 -4
When y = 0,
x2 = 9
So x = +3 or -3
When x = 0,
y2 = 9
So y = +3 or -3 x x x
We have 2 points
(0,3)
We have 2 points
(3,0)
and (-3,0)
and (0,-3) x

5. Equation Straight Line
y = mx + c
Where
m is the gradient or slope
c is the y-intercept

6. Consider y = 2x + 1 4 3 2 y intercept 1 Point (0,1) -1 x -2 -3 -4 4 3 2 1 -1 -2 -3 -4
y intercept
Point (0,1) x
Gradient = 2
Line rises 2 units for every 1 unit to the right

7. Solve these 2 equations simultaneously
Graphical method
May be required to draw one or both equations
Careful drawing required for accurate answer

8. …. Once drawn 4 1st Solution 3 x = 0.94 y = 2.85 2 1 -1 2nd Solution-2 -3 -4
1st Solution
x = 0.94
y = 2.85
2nd Solution
x = -1.75
y = -2.41

9. Algebraic Solution y = 2x + 1 x2 + y2 = 9 Substitute 2x + 1 for y
Expand (2x + 1)2
x2 + 4x2 + 4x + 1 = 9
Simplify
5x2 + 4x + 1 = 9
Rearrange
5x2 + 4x -8 = 0

10. Use formula 5x2 + 4x -8 = 0 So, x = -1.7266…. or 0.9266….
So, y = …. or ….
Solutions, (-1.73, -2.45) & (0.93,2.85) to 2d.p.