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

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Answer 1 · 2015-12-12T14:41:59

The solution for the system of equations is
$a = - 8, b = - 3$ $color(blue)(a=-8,b=-3$

$a = 3 b + 1$ $a=color(blue)(3b+1$ ........equation $(1)$ $(1)$

$5 b - 2 a = 1$ $5b-2a=1$ ......equation $(2)$ $(2)$

Solving by substitution

Substituting equation $1$ $1$ in $2$ $2$ :

$5 b - 2 a = 1$ $5b-2a=1$

$5 b - 2 \cdot (3 b + 1) = 1$ $5b-2 * (color(blue)(3b+1))=1$

$5 b - 6 b - 2 = 1$ $5b-6b-2=1$

$- b = 1 + 2$ $-b=1+2$

$b = - 3$ $color(blue)(b=-3$

Finding $a$ $a$ by substituting the value of $b$ $b$ in equation $1$ $1$ :

$a = 3 b + 1$ $a=3b+1$

$a = 3 \cdot - 3 + 1$ $a=3 * -3 +1$

$a = - 9 + 1$ $a=-9 +1$

$a = - 8$ $color(blue)(a=-8$