How do you solve by substitution $x + 2 y = 7$ $x + 2y = 7$ and $2 x + y = 8$ $2x + y = 8$ ?

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How do you solve by substitution $x + 2 y = 7$ $x + 2y = 7$ and $2 x + y = 8$ $2x + y = 8$ ?

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Answer 1 · 2015-06-07T12:05:55

$x + 2 y = 7$ $x + 2y = 7$
$x = 7 - 2 y$ $x =color(blue)( 7 - 2y$ ..........equation $(1)$ $(1)$

$2 x + y = 8$ $2x + y = 8$ ...........equation $(2)$ $(2)$

Substituting equation $(1)$ $(1)$ in $(2)$ $(2)$ to find $y$ $y$ :
$2 (7 - 2 y) + y = 8$ $2color(blue)((7-2y)) + y = 8$
$14 - 4 y + y = 8$ $14 - 4y + y = 8$
$14 - 3 y = 8$ $14 - 3y= 8$
$- 3 y = - 6$ $- 3y= -6$
$y = \frac{6}{3}, y = 2$ $y= 6/3 , color(purple)(y= 2$

Substituting $y$ $y$ in equation $1$ $1$ to find $x$ $x$
$x = 7 - 2 y$ $x =7 - 2y$
$x = 7 - 2.2 = 7 - 4$ $x =7 - 2.2 = 7-4$
$x = 3$ $color(purple)(x =3$

The solution for the system of equations is
$x = 3, y = 2$ $color(purple)(x = 3 , y=2$

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How do you solve by substitution $x + 2 y = 7$ $x + 2y = 7$ and $2 x + y = 8$ $2x + y = 8$ ?

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