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Use the substitution method to solve the system of equations. 3x + 7y = 1 y = x – 7
A. (3, –4)

B. (4, –3)

C. (2, –5)

D. (5, –2)

Respuesta :

jerome70
My answer is D.(5, -2)

Answer: The correct option is (D) (5, -2).

Step-by-step explanation:  We are given to use the method of substitution to solve the following system of equations :

[tex]3x+7y=1~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]3x+7y=1\\\\\Rightarrow 3x+7(x-7)=1\\\\\Rightarrow 3x+7x-49=1\\\\\Rightarrow 10x=50\\\\\Rightarrow x=\dfrac{50}{10}\\\\\Rightarrow x=5,[/tex]

and from equation (ii) again, we get

[tex]y=x-7=5-7=-2.[/tex]

Thus, the required solution is (x, y) = (5, -2).

Option (D) is CORRECT.

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