1.

Solve equations by using the substitution method.3x – 5y = -1 x – y = -1

Answer»

Given: 

3x – 5y = -1 ……. (1) 

x – y = -1 …….. (2) 

From equation (2), 

x – y = – 1

x = y – 1 

Substituting x = y – 1 in equation (1) we get 

3 (y – 1) – 5y = – 1 

⇒ 3y – 3 – 5y = -1 

⇒ – 2y = – 1 + 3 

⇒ 2y = – 2 

⇒ y = -1 

Substituting y = – 1 in equation (1) we get 

3x – 5 (- 1) = -1 

3x + 5 = – 1 

3x = – 1 – 5 

x = \(\frac{-6}{3}\) = -2 

∴ The solution is (-2, -1)

The given system of equations is

3x−5y=−1 ..... (i)

x−y=−1 ......(ii)

From (ii), we get

y=x+1

Substituting y=x+1 in (i), we get

3x-5(x+1)=-1

3x-5x-5=-1

-2x=-1+5

X=4/-2

X=-2

Putting x=−2 in y=x+1 we get y=−1.

Hence, the solution of the given system of equations is x=−2,y=−1.


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