How do you solve $3x + 7y = 18$ and $x + 2y = 5$ ?

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Answer 1 · 2016-06-14T02:25:18

The solution for the system of equations is:

$color(green)(x=-1$

$color(green)(y = 3$

$3x + 7y = 18$ ........equation $(1)$

$x + 2y = 5$
$color(blue)(x = 5 - 2y$ .............equation $(2)$

Substituting equation $2$ in equation $1:$

$3x + 7y = 18$

$3 xx (color(blue)( 5 - 2y)) + 7y = 18$

$15 - 6y + 7y = 18$

$15 + y = 18$

$y = 18 - 15$

$color(green)(y = 3$

Now we substitute the value of $y$ in equation $2$ to find $x:$

$color(blue)(x = 5 - 2y$

$x = 5 - 2 xx (3)$

$x = 5 - 6$

$color(green)(x=-1$

How do you solve 3x + 7y = 183x + 7y = 18 and x + 2y = 5x + 2y = 5?