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How do you solve by substitution $4 x - 7 y = 10$ $4x-7y=10$ and $y = x - 7$ $y= x-7$ ?

1 Answer

Jun 4, 2015

Given
[1] $XXXX$ $color(white)("XXXX")$ $4 x - 7 y = 10$ $4x-7y = 10$
[2] $XXXX$ $color(white)("XXXX")$ $y = x - 7$ $y = x-7$

Using [2] substitute $(x - 7)$ $(x-7)$ for $y$ $y$ in [1]
[3] $XXXX$ $color(white)("XXXX")$ $4 x - 7 (x - 7) = 10$ $4x - 7(x-7) = 10$

Simplifying
[4] $XXXX$ $color(white)("XXXX")$ $- 3 x + 49 = 10$ $-3x +49 = 10$
[5] $XXXX$ $color(white)("XXXX")$ $x = 13$ $x = 13$

Using [5] substitute $(13)$ $(13)$ for $y$ $y$ in [2]
[6] $XXXX$ $color(white)("XXXX")$ $y = (13) - 7$ $y = (13) -7$
[7] $XXXX$ $color(white)("XXXX")$ $y = 6$ $y= 6$

$(x, y) = (13, 6)$ $(x,y)=(13,6)$

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