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Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

If 2a + 3b ...

Question

If $2 a + 3 b = 12$ , and $3 b - 4 = 2$ , then find the value of $a$ .

2

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3

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4

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Solution

The correct option is B $3$
Let $2 a + 3 b = 12$ ......(1)
and $3 b - 4 = 2$ ......(2)
On solving (2), we get
$3 b - 4 = 2$
$\Rightarrow 3 b = 2 + 4$
$\Rightarrow 3 b = 6$
$\Rightarrow b = 2$
Putting $b = 2$ in equation (1)
$2 a + 3 b = 12$
$\Rightarrow 2 a + 3 (2) = 12$
$\Rightarrow 2 a = 12 - 6$
$\Rightarrow 2 a = 6$
$\Rightarrow a = 3$

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