What is the value of $a$ for the following equation: $3 a + 4 b = 13$ and $a + 3 b = 1$ ?
(Use cross multiplication method).

a = 5

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a = 6

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a = 7

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a = 8

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Solution

The correct option is C $a = 7$
Given:
$3 a + 4 b = 13$ ---(1)
$a + 3 b = 1$ ---(2)

Using formula for cross multiplication method:

$\frac{a}{(b_{1} c_{2} - b_{2} c_{1})} = \frac{b}{(c_{1} a_{2} - a_{1} c_{2})} = \frac{- 1}{(a_{1} b_{2} - a_{2} b_{1})}$

So, from equations (1) and (2) we can write the value of coefficient $a, b$ and $c$ .

$\frac{a}{4 \times 1 - 3 \times 13} = \frac{b}{13 \times 1 - 3 \times 1} = \frac{- 1}{3 \times 3 - 1 \times 4}$

$\frac{a}{4 - 39} = \frac{b}{13 - 3} = \frac{- 1}{9 - 4}$

$\frac{a}{- 35} = \frac{b}{10} = \frac{- 1}{5}$

$\frac{a}{- 35} = \frac{- 1}{5}$

$5 a = 35$

$a = 7$

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What is the value of a for the following equation: 3a+4b=13 and a+3b=1? (Use cross multiplication method).

What is the value of $a$ for the following equation: $3 a + 4 b = 13$ and $a + 3 b = 1$ ?
(Use cross multiplication method).