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Mathematics

Solve the following pair of (simultaneous) equations using method of elimination by substitution :

3x + 2y = 11

2x - 3y + 10 = 0

Linear Equations

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Answer

Given,

Equations : 3x + 2y = 11 and 2x - 3y + 10 = 0

⇒ 3x + 2y = 11

⇒ 3x = 11 - 2y

⇒ x = 11−2y3\dfrac{11 - 2y}{3} ……..(1)

Substituting value of x from equation (1) in 2x - 3y + 10 = 0,

⇒2×(11−2y3)−3y+10=0⇒22−4y3−3y+10=0⇒22−4y−9y+303=0⇒52−13y3=0⇒52−13y=0⇒13y=52⇒y=5213=4.\Rightarrow 2 \times \Big(\dfrac{11 - 2y}{3}\Big) - 3y + 10 = 0 \\[1em] \Rightarrow \dfrac{22 - 4y}{3} - 3y + 10 = 0 \\[1em] \Rightarrow \dfrac{22 - 4y - 9y + 30}{3} = 0 \\[1em] \Rightarrow \dfrac{52 - 13y}{3} = 0 \\[1em] \Rightarrow 52 - 13y = 0 \\[1em] \Rightarrow 13y = 52 \\[1em] \Rightarrow y = \dfrac{52}{13} = 4.

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

⇒x=11−2×43=11−83=33=1.\Rightarrow x = \dfrac{11 - 2 \times 4}{3} \\[1em] = \dfrac{11 - 8}{3} \\[1em] = \dfrac{3}{3} \\[1em] = 1.

Hence, x = 1 and y = 4.

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