How do solve the following linear system?: $x-y=11 , -4x-15y=-1$ ?

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Answer 1 · 2016-05-03T12:04:22

The solution for the system of equations is:
$color(green)( x = 166/ 19$
$color(green)(y = - 43/ 19$

$x - y = 11$ , multiplying by $4$

$color(blue)(4x) - 4y = 44$ ..............equation $(1)$

$color(blue)(- 4x) - 15y = -1$ .......equation $(2)$

Solving by elimination

Adding equations $1$ and $2$ , eliminates $color(blue)(4x)$

$cancelcolor(blue)(4x) - 4y = 44$
$cancelcolor(blue)(- 4x) - 15y = -1$

$-19y = 43$

$y = 43/ (-19)$

$color(green)(y = - 43/ 19$

Finding the value of $x$ from equation $1$ using the value of $y$ :

$x - y = 11$

$x = 11 + y$

$x = 11 color(green)(- 43/19$

$x = 209 / 19 color(green)(- 43/19$

$color(green)( x = 166/ 19$

How do solve the following linear system?: x-y=11 , -4x-15y=-1 x-y=11 , -4x-15y=-1 ?