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Mathematics

Assertion(A): If 8x + 7y = 37 and 7x + 8y = 38, then x = -2, y = 3.

Reason(R): ax + by = c and bx + ay = d is not simultaneous linear equations in two variables.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Linear Equations

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Answer

Given,

Equations: 8x + 7y = 37 and 7x + 8y = 38

⇒ 8x + 7y = 37

⇒ 8x = 37 - 7y

⇒ x = 37−7y8\dfrac{37 - 7y}{8}     …..(1)

Substituting value of x from equation (1) in 7x + 8y = 38, we get :

⇒7(37−7y8)+8y=38⇒259−49y8+8y=38⇒259−49y+64y8=38⇒259+15y=38×8⇒259+15y=304⇒15y=304−259⇒15y=45⇒y=4515=3.\Rightarrow 7\Big(\dfrac{37 - 7y}{8}\Big) + 8y = 38 \\[1em] \Rightarrow \dfrac{259 - 49y}{8} + 8y = 38 \\[1em] \Rightarrow \dfrac{259 - 49y + 64y}{8} = 38\\[1em] \Rightarrow 259 + 15y = 38 \times 8 \\[1em] \Rightarrow 259 + 15y = 304 \\[1em] \Rightarrow 15y = 304 - 259 \\[1em] \Rightarrow 15y = 45\\[1em] \Rightarrow y = \dfrac{45}{15} = 3.

Substituting value of y in equation (1), we get :

⇒x=37−7y8⇒x=37−7×38⇒x=37−218⇒x=168=2.\Rightarrow x = \dfrac{37 - 7y}{8} \\[1em] \Rightarrow x = \dfrac{37 - 7 \times 3}{8} \\[1em] \Rightarrow x = \dfrac{37 - 21}{8} \\[1em] \Rightarrow x = \dfrac{16}{8} = 2.

x = 2 and y = 3.

∴ Assertion (A) is false.

⇒ ax + by = c and bx + ay = d are simultaneous linear equations in two variables x and y.

∴ Reason (R) is false.

Hence, option 4 is the correct option.

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