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Mathematics

Solve the following simultaneous linear equations:

2x - 34y\dfrac{3}{4}y = 3

5x - 2y = 7

Linear Equations

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Answer

Given,

2x - 34y\dfrac{3}{4}y = 3 ………(i)

5x - 2y = 7 ……….(ii)

Multiplying eq. (i) by 5 and (ii) by 2 we get,

10x - 154y\dfrac{15}{4}y = 15 …….(iii)

10x - 4y = 14 ……..(iv)

Subtracting eq. (iv) from (iii),

⇒10x−154y−(10x−4y)=15−14⇒4y−154y=1⇒16y−15y4=1⇒y4=1⇒y=4.\Rightarrow 10x - \dfrac{15}{4}y - (10x - 4y) = 15 - 14 \\[1em] \Rightarrow 4y - \dfrac{15}{4}y = 1 \\[1em] \Rightarrow \dfrac{16y - 15y}{4} = 1 \\[1em] \Rightarrow \dfrac{y}{4} = 1 \\[1em] \Rightarrow y = 4.

Substituting value of y in eq. (ii) we get,

⇒ 5x - 2(4) = 7

⇒ 5x - 8 = 7

⇒ 5x = 15

⇒ x = 3.

Hence, x = 3 and y = 4.

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