How do solve the following linear system?: $5 x + y = 9, - 4 x + 9 y = 9$ $5x + y = 9 , -4x + 9y = 9$ ?

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Answer 1 · 2016-04-14T09:37:27

The solution for the system of equations is :
$x = \frac{72}{49}$ $x = 72 / 49$

$y = \frac{81}{49}$ $y = 81/49$

$5 x + y = 9$ $5x + y = 9$ , multiplying by $9$ $9$
$45 x + 9 y = 81$ $45x + color(blue)(9y) = 81$ ...............equation $(1)$ $(1)$

$- 4 x + 9 y = 9$ $-4x + color(blue)( 9y) =9$ ...............equation $(2)$ $(2)$

Solving by elimination

Subtracting equation $2$ $2$ from $1$ $1$ :

$45x + cancelcolor(blue)(9y) = 81$

$+4x - cancelcolor(blue)( 9y) = -9$

$49 x = 72$

$x = 72 / 49$

Finding $y$ from equation $1$
$45x + 9y = 81$

$9y = 81 - 45x$

$9y = 81 - 45 * ( 72 / 49)$

$9y = 3969/49 - ( 3240 / 49)$

$9y = 729 /49$

$y = 729 /(49 * 9 )$

$y = 81/49$

How do solve the following linear system?: 5x + y = 9 , -4x + 9y = 9 5x+y=9,−4x+9y=95x + y = 9 , -4x + 9y = 9 ?