KnowledgeBoat Logo
|

Mathematics

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

2x - 3y = 7
5x + y = 9

Linear Equations

13 Likes

Answer

Given,

Equations : 2x - 3y = 7 and 5x + y = 9

⇒ 2x - 3y = 7

⇒ 2x = 7 + 3y

⇒ x = 7+3y2\dfrac{7 + 3y}{2} ………..(1)

Substituting value of x from equation (1) in 5x + y = 9, we get :

⇒5×(7+3y2)+y=9⇒35+15y2+y=9⇒35+15y+2y2=9⇒35+17y=18⇒17y=18−35⇒17y=−17⇒y=−1717=−1.\Rightarrow 5 \times \Big(\dfrac{7 + 3y}{2}\Big) + y = 9 \\[1em] \Rightarrow \dfrac{35 + 15y}{2} + y = 9 \\[1em] \Rightarrow \dfrac{35 + 15y + 2y}{2} = 9 \\[1em] \Rightarrow 35 + 17y = 18 \\[1em] \Rightarrow 17y = 18 - 35 \\[1em] \Rightarrow 17y = -17 \\[1em] \Rightarrow y = -\dfrac{17}{17} = -1.

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

⇒x=7+3y2=7+3×−12=7−32=42=2.\Rightarrow x = \dfrac{7 + 3y}{2} \\[1em] = \dfrac{7 + 3 \times -1}{2} \\[1em] = \dfrac{7 - 3}{2} \\[1em] = \dfrac{4}{2} \\[1em] = 2.

Hence, x = 2 and y = -1.

Answered By

3 Likes

Related Questions