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