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Simultaneous Equations
Solving Simultaneous Equations by Substitution
Solving Simultaneous Equations by Elimination
Solving Simultaneous Equations by Drawing Graphs
If X + Y = 5, what are the values of X and Y?
Is it X = 4, Y = 1 ?
(or) X = 3, Y = 2 ?
(or) X = 2.5, Y = 2.5 ?
To find unique values of X and Y, we need one more equation, say X – Y = 3.
Equations X + Y = 5 and X – Y = 3 are called as Simultaneous Equations.
The solution of above equations is X = 4 and Y = 1.
How to find these values of X and Y?
Use an equation to find one variable in terms of another variable and substitute in the other equation.
X + Y = 5 ….(1)
X – Y = 3 ….(2)
From (2), we get, X = 3 + Y
Substitute X = 3 + Y in (1)
3 + Y + Y = 5
3 + 2Y = 5
2Y = 5 – 3
2Y = 2
Y = 1
Substitute Y = 1 in (1),
X + Y = 5
X + 1 = 5
X = 5 – 1
X = 4
By adding or subtracting given equations, eliminate one variable.
Before add or subtract, make the coefficient of the variable you wish to eliminate equal in both equations.
X + Y = 5 ….(1)
X – Y = 3 ….(2)
(1) + (2), 2X = 8
X = 8/2 = 4
Substitute X = 4 in (1),
X + Y = 5
4 + Y = 5
Y = 5 – 4
Y = 1
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