Mathematics

Solve the following pairs of linear (simultaneously) equations using method of elimination by substitution:
y = 4x - 7
16x - 5y = 25

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Given,

Equations :

⇒ y = 4x - 7 ………(1)

⇒ 16x - 5y = 25 …….(2)

Substituting value of y from equation (1) in (2), we get :

⇒ 16x - 5(4x - 7) = 25

⇒ 16x - 20x + 35 = 25

⇒ -4x = 25 - 35

⇒ -4x = -10

⇒ 4x = 10

⇒ x = $\dfrac{10}{4} = \dfrac{5}{2}$ .

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

$\Rightarrow y = 4 \times \dfrac{5}{2} - 7 \\[1em] \Rightarrow y = 10 - 7 = 3.$

Hence, x = $\dfrac{5}{2}$ and y = 3.

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