How do you solve the system of equations: 5x + 3y = 12 ; 4x - 5y = 17?

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Answer 1 · 2015-08-22T07:50:04

The solutions are
$color(blue)(y=-1,x=3$

$5x + 3y = 12$ , multiplying by $4$
$color(blue)(20x) + 12y = 48$ ....equation $1$

$4x - 5y = 17$ , multiplying by $5$
$color(blue)(20x) - 25y = 85$ .....equation $2$

Solving by elimination

Subtracting equation $1$ from $2$

$cancelcolor(blue)(20x) + 12y = 48$
$cancel(-color(blue)(20x)) + 25y = -85$

$37y=-37$
$color(blue)(y=-1$

Finding $x$ from equation $1$
$5x + 3y = 12$

$5x = 12-3y$

$5x = 12+3$

$5x = 15$
$color(blue)(x=3$