How do you solve the system $3x-2y=2$ and $5x-5y=10$ ?

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Answer 1 · 2015-06-10T17:45:39

The solution for the system of equation is
$color(red)(x = -2 , y=-4$

$3x-2y=2$ ,multiplying the equation by $5$
$15x -color(red)( 10y) = 10$ ...........equation $1$

$5x-5y=10$ , multiplying the equation by $2$
$10x - color(red)(10y) = 20$ .......equation $2$

Subtracting equation $1$ from $2$ to eliminate $color(red)(10y$
$10x - cancelcolor(red)(10y) = 20$
$-15x +cancelcolor(red)( 10y) =- 10$

$-5x = 10$
$color(red)( x = -2$

Substituting $x$ in equation $1$ to find $y$
$3x - 2 = 2y$
$(3x-2)/2 =y$

$y = (3.(-2) - 2)/2$
$y = -8/2 = -4$
$color(red)(y=-4$

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