How do you solve the following system?: $2 x + y = 3, 2 y = 5 x - 3$ $2x+y=3 , 2y=5x-3$

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Answer 1 · 2016-03-03T18:25:56

The solution for the system of equations is:
$x = 1$ $color(blue)(x=1$
$y = 1$ $color(blue)(y=1$

$2 x + y = 3$ $2x +y=3$ , multiplying by $2$ $2$
$4 x + 2 y = 6$ $4x +color(blue)(2y)=6$ .......equation $(1)$ $(1)$

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

Solving by elimination

Adding equations $(2)$ $(2)$ and $(1)$ $(1 )$ results in elimination of $2 y$ $color(blue)(2y$

$4x +cancelcolor(blue)(2y)=6$

$5x-cancelcolor(blue)(2y)=3$

$9x=9$

$x=9/9$

$color(blue)(x=1$

Finding $y$ from equation $1$ :
$2x +y=3$

$y=3 - 2x$

$y=3 - 2 xx 1$

$y=3 - 2$

$color(blue)(y=1$

How do you solve the following system?: 2x+y=3 , 2y=5x-3 2x+y=3,2y=5x−3 2x+y=3 , 2y=5x-3