How do you solve $7 x - y = 26$ $7x - y = 26$ and $x + y = 6$ $x + y = 6$ using substitution?

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Answer 1 · 2016-05-11T04:59:57

The solution for the system of equations is :
$x = 4$ $color(green)(x= 4$

$y = 2$ $color(green)(y=2$

$7 x - y = 26$ $7x - y = 26$ .........equation $(1)$ $(1)$

$x + y = 6$ $x + y = 6$ ,
$y = 6 - x$ $color(blue)(y = 6 - x$ ..............equation $(2)$ $(2)$

Solving by substitution :

Substituting equation $2$ $2$ in equation $1$ $1$ :

$7 x - y = 26$ $7x - y = 26$

$7 x - (6 - x) = 26$ $7x - color(blue)((6 - x))= 26$

$7 x - 6 + x = 26$ $7x - 6 + x= 26$

$7 x + x = 26 + 6$ $7x + x= 26 + 6$

$8 x = 32$ $8x= 32$

$x = \frac{32}{8}$ $x= 32/8$

$x = 4$ $color(green)(x= 4$

Finding $y$ $y$ from equation $2$ $2$
$y = 6 - x$ $color(blue)(y = 6 - x$

$y = 6 - 4$ $y = 6 - 4$

$y = 2$ $color(green)(y=2$

The solution for the system of equations is :
$x = 4$ $color(green)(x= 4$

$y = 2$ $color(green)(y=2$

How do you solve 7x−y=267x - y = 26 and x+y=6x + y = 6 using substitution?