Question

Solve x+y=14 x-y=4 by subtituion method

Answer 1

x+y=14 .....1

x-y=4 .....2

x-y=4

x=y+4

Put x=y+4 in equation 1.

y+4+y=14

2y=10

y=5

x=y+4

x=5+4

x=9

x=9,y=5

Answer 2

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$\rm\:x+y=14\:.......................(i)$

$\rm\:x-y=4\:.........................(ii)$

From equation (i),

$\rm\:x+y=14$

$\rm\:x=14-y\:......................(iii)$

Putting the value of x in equation (ii),

$\rm\:x-y=4$

$\rm\longrightarrow\:14-y-y=4$

$\rm\longrightarrow\:14-2y=4$

$\rm\longrightarrow\:-2y=4-14$

$\rm\longrightarrow\:-2y=-10$

$\rm\longrightarrow\:y=\cancel\dfrac{-10}{-2}$

$\rm\longrightarrow\:y=5$

putting the value of y in equation (iii),

$\rm\:x=14-y$

$\rm\longrightarrow\:x=14-5$

$\rm\longrightarrow\:x=9$

Hence,the value of x is 9 and value of y is 5.

❍ Substitution method :-

☛ suppose we are given two linear equations in x and y for solving this equation by the substitution method,we proceed according to the following steps.

1 ✎ Express y in term of x in one of the given equation.

2 ✎ substitute this value of y in terms of x in the other equation.This gives a linear equation in x.

3 ✎ solve the linear equation in x obtained in step 2.

4 ✎ substitute this value of x in the relation taken in step 1 to obtained a linear equation in y.

5 ✎ solve the above linear equation in y to get the value of y.