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How do you solve the system 7r-2s=33 and 2r+7s=70?

1 Answer

Aug 22, 2015

The solutions are
$s = 8, r = 7$ $color(blue)(s=8,r=7$

Explanation:

$7 r - 2 s = 33$ $7r-2s=33$ , multiplying by $2$ $2$
$14 r - 4 s = 66$ $color(blue)(14r)-4s=66$ .....equation $1$ $1$

$2 r + 7 s = 70$ $2r+7s=70$ , multiplying by $7$ $7$
$14 r + 49 s = 490$ $color(blue)( 14r)+49s=490$ .....equation $2$ $2$

Solving by elimination
Subtracting equation $2$ $2$ from $1$ $1$
$14 r - 4 s = 66$ $color(blue)(14r)-4s=66$
$cancelcolor(blue)( -14r)-49s=-490$

$-53s=-424$
$color(blue)(s=8$

Finding $r$ from equation $1$
$7r-2s=33$
$7r=33+2s$
$7r=33+16$
$7r=49$
$color(blue)(r=7$

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