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Mathematics

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

2x + 7y = 39
3x + 5y = 31

Linear Equations

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Answer

Given,

Equations : 2x + 7y = 39 and 3x + 5y = 31

⇒ 2x + 7y = 39

⇒ 2x = 39 - 7y

⇒ x = 39−7y2\dfrac{39 - 7y}{2} ……..(1)

Substituting value of x from equation (1) in 3x + 5y = 31, we get :

⇒3×39−7y2+5y=31⇒117−21y2+5y=31⇒117−21y+10y2=31⇒117−11y=62⇒11y=117−62⇒11y=55⇒y=5511=5.\Rightarrow 3 \times \dfrac{39 - 7y}{2} + 5y = 31 \\[1em] \Rightarrow \dfrac{117 - 21y}{2} + 5y = 31 \\[1em] \Rightarrow \dfrac{117 - 21y + 10y}{2} = 31 \\[1em] \Rightarrow 117 - 11y = 62 \\[1em] \Rightarrow 11y = 117 - 62 \\[1em] \Rightarrow 11y = 55 \\[1em] \Rightarrow y = \dfrac{55}{11} = 5.

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

⇒x=39−7×52⇒x=39−352⇒x=42=2.\Rightarrow x = \dfrac{39 - 7 \times 5}{2} \\[1em] \Rightarrow x = \dfrac{39 - 35}{2} \\[1em] \Rightarrow x = \dfrac{4}{2} = 2.

Hence, x = 2 and y = 5.

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