Question

if 3a+5b=9 and 5a+3b=7. What is the value of a+b​

Answer 1

Step-by-step explanation:

(3a +5b) ×3 = 9×3

(5a +3b) ×5 = 7×5

9a+15b=27

25a+15b=35

-16a = -8

a=1/2

9/2 +15b=27

b=3/2

a+b= 1/2 +3/2

= 2

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Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

$\sf = > 3a + 5b = 9..... \times 5$

$\sf= > 5a + 3b = 7.... \times 3$

=>15a+25b=45

=>15a+9b=21

=>(-)....(-)......(-)

____________

16b=24

$\sf = > b = \dfrac{24}{16} = \dfrac{6}{4} = \dfrac{3}{2}$

$\sf \bold{b = \dfrac{3}{2}}$

Put b's Value in the Equation 3a+5b=9

$\sf= > 3a + 5 \times \dfrac{3}{2} = 9$

$\sf= > 3a + \dfrac{15}{2} = 9$

$\sf = > 3a = 9 - \dfrac{15}{2} = \dfrac{18 - 15}{2}$

$\sf= > 3a = \dfrac{3}{2}$

$\sf = > a = \dfrac{3}{2} \div 3$

$= > a = \dfrac{3}{2} \times \dfrac{1}{3} = \dfrac{3}{6} = \dfrac{1}{2}$

$\sf\bold{a = \dfrac{1}{2}}$

$\sf\bold{\boxed{{a = \dfrac{1}{2}} \sf \bold{,b = \dfrac{3}{2}}}}$