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

Question

2579 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-05T17:38:59

The solution for the system of equations is

$x = \frac{13}{5}, y = \frac{1}{5}$ $color(blue)(x=13/5, y=1/5$

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

$x + 2 y = 3$ $x +2y=3$ , multiplying by $2$ $2$

$2 x + 4 y = 6$ $color(blue)(2x) +4y=6$ ....equation $(2)$ $(2)$

Solving by elimination

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

$cancelcolor(blue)(2x)-y=5$
$-cancelcolor(blue)(2x) -4y=-6$

$-5y=-1$

$y=(-1)/(-5)$

$color(blue)(y=1/5$

Finding $x$ from equation $2$

$x +2y=3$

$x =3-2y$

$x =3-2 xx (1/5)$

$x =3-2/5$

$x =15/5-2/5$

$color(blue)(x =13/5$

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