Question
For solving pair of equation, in this exercise use the method of elimination by equating coefficients :$41x + 53y = 135;53x + 41y = 147$
✓
Answer
$41x + 53y = 135 \dots...(1)$
$53x + 41y = 147 \dots...(2)$
Adding equation $(1)$ and $(2)$
$41x + 53y = 135$
$+ 53x + 41y = 147$
$94x + 94y = 282$
Dividing by $94,$
$x + y = 3\dots ....(3)$
Subtracting equation $(2)$ from $(1)$
$41x + 53y = 135$
$- 53x + 41y = 147 $
$- - - $
$- 12x + 12y = - 12$
Dividing by $12,$
$- x + y = -1\dots....(4)$
Adding $(3)$ and $(4)$
$x + y = 3$
$+ - x + y = -1$
$2y = 2$
$y = 1$
From $(3)$
$x + y = 3$
$x + 1 = 3$
$x = 2$
$53x + 41y = 147 \dots...(2)$
Adding equation $(1)$ and $(2)$
$41x + 53y = 135$
$+ 53x + 41y = 147$
$94x + 94y = 282$
Dividing by $94,$
$x + y = 3\dots ....(3)$
Subtracting equation $(2)$ from $(1)$
$41x + 53y = 135$
$- 53x + 41y = 147 $
$- - - $
$- 12x + 12y = - 12$
Dividing by $12,$
$- x + y = -1\dots....(4)$
Adding $(3)$ and $(4)$
$x + y = 3$
$+ - x + y = -1$
$2y = 2$
$y = 1$
From $(3)$
$x + y = 3$
$x + 1 = 3$
$x = 2$
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