Question

Find the Solution of the following pair of linear equations.

x+ y = 16, x – y = 4

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Answer 1

Answer:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation

x+y=16,x−y=4

Choose one of the equations and solve it for xx by isolating xx on the left hand side of the equal sign.

x+y=16

Subtract yy from both sides of the equation.

x=−y+16

Substitute -y+16−y+16 for xx in the other equation, x-y=4x−y=4.

−y+16−y=4

Add -y−y to -y−y.

-2y+16=4

Subtract 1616 from both sides of the equation.

-2y=-12

Divide both sides by -2−2.

y=6

Add 1616 to -6−6.

x=10

The system is now solved.

x=10,y=6

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Answer 2

✯ Given :-

■ x + y = 16

■ x - y = 4

✯ To Find :-

■ What is the value of x

✯ Method Used :-

■ Substitution Method

✯ Solution :-

Given equation :

x + y = 16 .... ❶

x - y = 4 .... ❷

From the equation no (1) we get,

⇒ x + y = 16

⇒ x = 16 - y

Substituting x = 16 - y in the equation no (2) we get,

⇒ x - y = 4

⇒ (16 - y) - y = 4

⇒ 16 - y - y = 4

⇒ 16 - 2y = 4

⇒ - 2y = 4 - 16

⇒ - 2y = - 12

⇒ y = $\dfrac{- 12}{- 2}$

➥ y = 6

Putting y = 6 in the equation no (2) we get,

⇒ x - y = 4

⇒ x - 6 = 4

⇒ x = 4 + 10

➥ x = 10

$\therefore$ The value of x is 10 and the value of y is 6 .

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