How do you solve the system $5 x + 3 y = 3$ $5x + 3y =3$ and $x + 9 y = 2$ $x+ 9y = 2$ ?

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How do you solve the system $5 x + 3 y = 3$ $5x + 3y =3$ and $x + 9 y = 2$ $x+ 9y = 2$ ?

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Answer 1 · 2015-06-02T16:10:56

$5 x + 3 y = 3$ $5x+ 3y =3$ ......equation $(1)$ $(1)$
$x + 9 y = 2$ $x+ 9y = 2$
$x = 2 - 9 y$ $x=color(blue)( 2-9y$ .........equation $(2)$ $(2)$

Solving by substitution
substituting equation $(2)$ $(2)$ in equation $(1)$ $(1)$

$5 x + 3 y = 3$ $5x + 3y =3$
$5 (2 - 9 y) + 3 y = 3$ $5color(blue)((2-9y)) + 3y =3$
$10 - 45 y + 3 y = 3$ $10 - 45y+ 3y =3$
$- 42 y = - 7$ $-42y=-7$
$y = \frac{1}{6}$ $color(blue)(y)=1/6$

finding the value of $x$ $x$ by substituting the value of $y$ $y$ in equation $(2)$ $(2)$
$x = 2 - 9 y$ $x= 2-9y$
$x = 2 - 9 (\frac{1}{6})$ $x= 2-9(1/6)$
$x = \frac{12 - 9}{6} = \frac{3}{6} = \frac{1}{2}$ $color(blue)(x)= (12-9)/6 = 3/6 = 1/2$

the solution for the system of equations is
$x = \frac{1}{2}, y = \frac{1}{6}$ $color(blue)( x = 1/2 , y =1/6$

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How do you solve the system $5 x + 3 y = 3$ $5x + 3y =3$ and $x + 9 y = 2$ $x+ 9y = 2$ ?

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