How do you solve $2a + 3b = -1$ and $3a + 5b = -2$ ?

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Answer 1 · 2015-08-21T07:13:12

The solutions are
$color(blue)(a=1,b=-1$

$2a+3b=−1$ , multiplying the equation by $3$
$color(blue)(6a)+9b=−3$ ..........equation $1$

$3a+5b=−2$ multiplying the equation by $2$
$color(blue)( 6a)+10b=−4$ .......equation $2$

Solving by elimination .
Subtracting equation $2$ form $1$

$cancel( color(blue)(6a))+9b=−3$
$cancel(-color(blue)( 6a))-10b=+4$

$-b=1$
$color(blue)(b=-1$

Substituting $b$ in equation $1$ to find $a$ :
$2a+3b=−1$
$2a=−1-3b$
$2a=−1-3*(-1)$
$2a=2$
$color(blue)(a=1$

How do you solve 2a + 3b = -12a + 3b = -1 and 3a + 5b = -23a + 5b = -2?