Question

lf 3x + 5y=9 & 5x+3y=7 then find value of x+y

Answer 1

3x+5y=9 (add the equations)
5x+3y=7
8x+8y=16 ÷8
x+y=2 equation (1)

3x+5y=9
5x+3y=7 (now subtract both equation)
-2x+2y=2 ÷2
-x+y=1 equation(2)
from equation 1 and 2

x+y=2
-x+y=1
2y=3
y=3/2

subyitute y in equation (1)
x+y=2
x=2-3/2
x=4-3/2
x=1/2

x+y=1/2+3/2=4/2=2
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Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given :- \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \text{ 3x + 5y = 9 \: \: \: - - - - - - > (1) } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \text{5x + 3y = 7 \: \: \: - - - - - - >(2) \: } \\ \\ \underline{ \mathfrak{ \: \: To \: \: find :- \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \text{ \huge{ x + y = ?}}$

$\underline{ \mathfrak { \:Now,\:}} \\ \\ \rm{(1) \times 3 \implies 9x + 15y = 27 \: \: - - - - > (3)} \\ \\ \rm{(2) \times 5 \implies 25x + 15y = 35 \: \: - - - - > (4)}$

$\sf{(4) - (3) \implies \: 16x = 8} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \implies \: x = \frac{8}{16} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ \therefore \: \red{x = \frac{1}{2}} }$

$\underline{ \text{ \: Putting the value of \: \red{x} \: in eq. (1) , we get, \: }}$

$\: \: \: \: \: \: \: \: \: \sf{ 3 \times ( \red{\frac{1}{2}} ) + 5y = 9 }\\ \\ \sf{\implies \: \frac{3}{2} + 5y = 9 }\\ \\ \sf{\implies \: 5y = 9 - \frac{3}{2}} \\ \\ \sf{ \implies \: 5y = \frac{18 - 3}{2}} \\ \\ \sf{\implies \: 5y = \frac{15}{2}} \\ \\ \sf{ \implies \: y = \frac{15}{2} \times \frac{1}{5} } \\ \\ \: \: \: \: \: \: \: \: \: \: \sf{\therefore \: \red{ y = \frac{3}{2} }}$

$\tt{ \therefore \: \pink{ x + y = \frac{1}{2} + \frac{3}{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \pink{ = \frac{1 + 3}{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \pink{ = \frac{4}{2} }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \pink{ =2 }}$

$\: \: \: \: \: \: \: \:\: \: \huge{ \therefore \: \boxed{ \bold{ \green{ \: x + y = 2 \: }}}}$