How do you solve the following linear system: $y = 2 x - 1, x - y = 5$ $y=2x-1, x-y=5$ ?

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Answer 1 · 2015-12-13T03:47:14

The solution for the system of equations is
$x = - 4, y = - 9$ $color(blue)(x=-4,y=-9$

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

$x - y = 5$ $x-y=5$ .........equation $(2)$ $(2)$

Solving by substitution.

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

$x - y = 5$ $x-y=5$

$x - (2 x - 1) = 5$ $x-color(blue)((2x-1)=5$

$x - 2 x + 1 = 5$ $x-2x +1=5$

$- x + 1 = 5$ $-x +1=5$

$- x = 5 - 1$ $-x =5-1$

$- x = 4$ $-x =4$

$x = - 4$ $color(blue)(x =-4$

Finding $y$ $y$ by substituting $x$ $x$ in equation $1$ $1$ :

$y = 2 x - 1$ $color(blue)(y=2x-1$

$y = 2 \cdot (- 4) - 1$ $y=2*(-4)-1$

$y = - 8 - 1$ $y=-8-1$

$y = - 9$ $color(blue)(y=-9$

How do you solve the following linear system: y=2x-1, x-y=5 y=2x−1,x−y=5 y=2x-1, x-y=5 ?