Quadratic Equations And Cubic Equations Worksheet With Answers Page 6
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Simultaneous Equations
3.1
Simultaneous linear equations in two variables
The general form of simultaneous linear equations in two variables is
ax + by = c
dx + ey = f
where x,y are variables, a,b,c,d,e,f are constants.
Various methods exist for solving these equations for x and y. These are:
(i) elimination method
(ii) substitution method
(iii) matrix method and
(iv) graphical method.
The reader is encouraged to find out.
3.2
Simultaneous equations, atleast one non-linear
The general form of simultaneous equations in which one is linear one is
quadratic is
ax + bx = c
2
2
dx
+ exy + f y
= g
where x,y are variables, and a,b,c,d,e,f ,g are arbitrary constants.
Example: Solve the simultaneous equations for x and y.
2
2
x
+ y
= 25
(1)
x + 3y = 5
(2)
From (2), x=5-3y.
Substitute for x in (2),
2
2
(5
3y)
+ y
= 25
2
y
3y = 0
y(y
3) = 0
either y = 0 or y = 3.
Hence, x = 5 when y = 0 or
x =
4 when y = 3.
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