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Mathematics

Solve the following pairs of linear (simultaneously) equations using method of elimination by substitution:

8x + 5y = 9
3x + 2y = 4

Linear Equations

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Answer

Given,

Equations : 8x + 5y = 9 and 3x + 2y = 4

⇒ 8x + 5y = 9

⇒ 8x = 9 - 5y

⇒ x = 9−5y8\dfrac{9 - 5y}{8} ……….(1)

Substituting value of x from equation (1) in 3x + 2y = 4, we get :

⇒3×(9−5y8)+2y=4⇒27−15y8+2y=4⇒27−15y+16y8=4⇒⇒27+y=32⇒y=32−27=5.\Rightarrow 3 \times \Big(\dfrac{9 - 5y}{8}\Big) + 2y = 4 \\[1em] \Rightarrow \dfrac{27 - 15y}{8} + 2y = 4 \\[1em] \Rightarrow \dfrac{27 - 15y + 16y}{8} = 4 \\[1em] \Rightarrow \Rightarrow 27 + y = 32 \\[1em] \Rightarrow y = 32 - 27 = 5.

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

⇒x=9−5×58=9−258=−168=−2.\Rightarrow x = \dfrac{9 - 5 \times 5}{8} \\[1em] = \dfrac{9 - 25}{8} \\[1em] = -\dfrac{16}{8} \\[1em] = -2.

Hence, x = -2 and y = 5.

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