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One Linear and One Quadratic Simultaneous Equations
Example:
Choose the linear equation
and rearrange to make
either x or y the subject
Substitute into the quadratic
equation and simplify
Linear equation is
2x  3y  2
 2  3y 
2
4
 y 4
 2 
10 y 2  6 y  0
2
Re-arranging:
42  3y
 y2  4
4
2y  0
2  3y
 y2  4
or 5 y  6  0
2x  3y  2
4x  y  4
2
2
2x  2  3y
2  3y
x
2
2
2
9 y2  6 y  4  y2  4  0
10 y  6 y  0
2
x y 3
x2  y 2  5
yx4
2 x 2  xy  1
Solve the resulting
quadratic equation
2 y 5 y  6  0
y  0, y  6
Substitute back into rearranged
linear equation to get other
values
2  3y
x
2
2
When y  0, x   1
2
2  3 65 
When y  6 5 , x 
3
x
5
2  185 10  18 8 4



2
10
10 5
Write down
your pairs of
solutions
1,0
or
 4 5 , 6 5 
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