Solve the pair of linear equations by substitution method: x + y … - Vidyadip

Question

Solve the pair of linear equations by substitution method: x + y = 14; x – y = 4

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Answer

x + y = 14; x - y = 4
the given pair of linear equations is
x + y = 14.................(1)
x - y = 4....................(2)
From equation(1),
y = 14 - x...................(3)
Substitute this value of y in equation(2), we get
x - (14 - x) = 4
$\Rightarrow$ x - 14 + x = 4
$\Rightarrow$2x - 14 = 4
$\Rightarrow$2x = 4 + 14
$\Rightarrow$2x = 18
$\Rightarrow x = \frac { 18 } { 2 } = 9$
Substituting this value of x in equation (3), we get y = 14 - 9 = 5
Therefore, the solution is x = , y = 5
verification: Substituting x = 9 and y = 5, we find that both the equations (1) and (2) are satisfied as shown below:
x + y = 9 + 5 = 14
x - y = 9 - 5=4
This verifies the solution.

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