Question

2a+3b=2 & 4a+9b=-1 by substitution method​

Answer 1

Answer:

By first equation

$2a + 3b = 2 \\ 2a = 2 - 3b \\ 4a = 4 - 6b$

In second equation.

$4a + 9b = - 1 \\ 4 - 6b + 9b = - 1 \\ 4 + 3b = - 1 \\ 3b = - 5 \\ b = \frac{ - 5}{4}$

and

$a = \frac{2 - 3b}{2} \\ a = 1 - \frac{3}{2} \times \frac{ - 5}{4} \\ a = 1 + \frac{15}{8} \\ a = \frac{23}{8}$

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Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

2a + 3b = 2

4a + 9b = -1

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The value of a and b.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have;

$\bullet\sf{2a+3b=2........................(1)}\\\bullet\sf{4a+9b=-1.....................(2)}$

$\bf{\underline{\underline{\bf{Using\:Substitution\:Method\::}}}}}$

From equation (1),we get;

$\longrightarrow\sf{2a+3b=2}\\\\\longrightarrow\sf{2a=2-3b}\\\\\longrightarrow\sf{a=\dfrac{2-3b}{2} ........................(3)}$

Putting the value of a in equation (2),we get;

$\longrightarrow\sf{4\bigg(\dfrac{2-3b}{2} \bigg)+9b=-1}\\\\\\\longrightarrow\sf{\dfrac{8-12b}{2} +9b=-1}\\\\\\\longrightarrow\sf{8-12b+18b=-2}\\\\\\\longrightarrow\sf{8+6b=-2}\\\\\\\longrightarrow\sf{6b=-2-8}\\\\\\\longrightarrow\sf{6b=-10}\\\\\\\longrightarrow\sf{b=-\cancel{\dfrac{10}{6} }}\\\\\\\longrightarrow\sf{\green{b=-\dfrac{5}{3} }}$

Putting the value of b in equation (3),we get;

$\longrightarrow\sf{a=\dfrac{2-3\big(-\dfrac{5}{3}\big) }{2} }\\\\\\\longrightarrow\sf{a=\frac{2-\big(-\dfrac{15}{3} \big)}{2} }\\\\\\\longrightarrow\sf{a=\dfrac{\frac{6+15}{3} }{2} }\\\\\\\longrightarrow\sf{a=\dfrac{21}{\frac{3}{2} } }\\\\\\\longrightarrow\sf{a=\cancel{\dfrac{21}{3} }\times \dfrac{1}{2} }\\\\\\\longrightarrow\sf{\green{a=\dfrac{7}{2} }}$

Thus;

The value of a is 7/2 and b is -5/3 .