How do you solve 9x - 3y = 3 and 3x + 8y = -17?

Question

3950 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-05T07:29:51

The solution is
$x = - \frac{1}{3}, y = - 2$ $color(blue)(x=-1/3, y=-2$

$9 x - 3 y = 3$ $color(blue)(9x) - 3y = 3$ ..........equation $1$ $1$

$3 x + 8 y = - 17$ $3x + 8y = -17$ , multiplying the equation by $3$ $3$
$9 x + 24 y = - 51$ $color(blue)(9x) + 24y = -51$ ......equation $2$ $2$

Solving by elimination .
Subtracting equation $2$ $2$ from $1$ $1$ results in elimination of $9 x$ $color(blue)(9x$

$cancelcolor(blue)(9x) - 3y = 3$

$-cancelcolor(blue)(9x) - 24y = +51$

$-27y =54$
$color(blue)(y=-2$

Finding $x$ by substituting $y$ in equation $1$
$9x - 3y = 3$

$x = (3+3y)/9$

$x = (3+3*(-2))/9$

$x = (3-6)/9$

$x = (-3)/9$

$color(blue)(x =-1/3$