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

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

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Answer 1 · 2017-01-19T14:42:30

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

Explanation:

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

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

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

Putting this in (B), we get $4 \times 2 + 3 b = 17$ $4xx2+3b=17$

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

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

$5 c - 2 \times 2 = 1$ $5c-2xx2=1$

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

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

Answer 2 · 2017-01-19T14:48:32

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

Explanation:

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

$2 a - 3 b = - 5 \times x \to (1)$ $2a-3b=-5color(white)(xxx)to(1)$
$4 a + 3 b = \times 17 \times \to (2)$ $4a+3b=color(white)(xx)17color(white)(xx) to(2)$
$---------------------$ $"---------------------"$
$6 a + 0 x = \times 12 \Rightarrow a = 2$ $6a+0color(white)(x)=color(white)(xx)12rArra=2$

Substitute a = 2 into (2)

$(4 \times 2) + 3 b = 17 \Rightarrow 8 + 3 b = 17$ $(4xx2)+3b=17rArr8+3b=17$

$\Rightarrow 3 b = 17 - 8 = 9 \Rightarrow b = 3$ $rArr3b=17-8=9rArrb=3$

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

$\Rightarrow 5 c - (2 \times 2) = 1 \Rightarrow 5 c - 4 = 1$ $rArr5c-(2xx2)=1rArr5c-4=1$

$\Rightarrow 5 c = 1 + 4 = 5 \Rightarrow c = 1$ $rArr5c=1+4=5rArrc=1$

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

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

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