# Solve the equations 2a-3b=-5, 4a+3b=17 and 5c-2a=1?

Jan 19, 2017

$a = 2$, $b = 3$ and $c = 1$

#### Explanation:

$2 a - 3 b = - 5$ ....................................(A)
$4 a + 3 b = 17$ ....................................(B)
$5 c - 2 a = 1$ ....................................(C)

Adding (A) and (B), we get $2 a - 3 b + 4 a + 3 b = - 5 + 17$

i.e. $6 a = 12$ i.e. $a = \frac{12}{6} = 2$

Putting this in (B), we get $4 \times 2 + 3 b = 17$

or $8 + 3 b = 17$ i.e. $3 b = 17 = 8 = 9$ and $b = \frac{9}{3} = 3$

and putting value of $a$ in (C), we get

$5 c - 2 \times 2 = 1$

or $5 c - 4 = 1$ i.e. $5 c = 1 + 4 = 5$ i.e. $c = 1$

and $a = 2$, $b = 3$ and $c = 1$

Jan 19, 2017

$a = 2 , b = 3 , c = 1$

#### Explanation:

If we add the first 2 equations, we will eliminate b and be able to solve for a

$2 a - 3 b = - 5 \textcolor{w h i t e}{\times x} \to \left(1\right)$
$4 a + 3 b = \textcolor{w h i t e}{\times} 17 \textcolor{w h i t e}{\times} \to \left(2\right)$
$\text{---------------------}$
$6 a + 0 \textcolor{w h i t e}{x} = \textcolor{w h i t e}{\times} 12 \Rightarrow a = 2$

Substitute a = 2 into (2)

$\left(4 \times 2\right) + 3 b = 17 \Rightarrow 8 + 3 b = 17$

$\Rightarrow 3 b = 17 - 8 = 9 \Rightarrow b = 3$

Substitute a = 2 into the third equation and solve for c

$\Rightarrow 5 c - \left(2 \times 2\right) = 1 \Rightarrow 5 c - 4 = 1$

$\Rightarrow 5 c = 1 + 4 = 5 \Rightarrow c = 1$

$\text{Thus " a=2,b=3" and } c = 1$