How do you solve the system of linear equations $2x + 5y = 8$ and $-3x + y = 5$ ?

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Answer 1 · 2016-05-10T08:12:36

The solution for the system of equations is
$color(blue)(x = -1 , y = 2$

$2x + color(green)(5y) = 8$ ........equation $(1)$

$-3x + y = 5$ , multiplying by $5$
$-15x + color(green)(5y) = 2 5$ .......equation $(2)$

Solving by elimination:

Subtracting equation $2$ from $1$ :

$2x + cancelcolor(green)(5y) = 8$
$+15x - cancelcolor(green)(5y) = -2 5$

$17x = -17$

$x = (-17) / 17$

$color(blue)(x = -1$

Finding $y$ from equation $2$

$-3x + y = 5$

$y = 5 + 3x$

$y = 5 + 3 * (-1)$

$y = 5 - 3$

$color(blue)(y =2$

The solution for the system of equations is
$color(blue)(x = -1 , y = 2$

How do you solve the system of linear equations 2x + 5y = 82x + 5y = 8 and -3x + y = 5-3x + y = 5?