Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y + 4x = 18 2y – 3x = 4 A. (6, –3) B. (3, 3) C. (2, 5) D. (5, –1)

Question

asked Jan 27, 2019 34.8k views

2 Answers

Darb · Answer 1 · 2019-02-01T02:33:52+0000

Answer: the correct option is (C) (2, 5).

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

$2y+4x=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2y-3x=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Dividing equation equation (i) on both sides by 2, we have

$(2y+4x)/(2)=(18)/(2)\\\\\Rightarrow y+2x=9\\\\\Rightarrow y=9-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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

$2(9-2x)-3x=4\\\\\Rightarrow 18-4x-3x=4\\\\\Rightarrow 18-4=4x+3x\\\\\Rightarrow 14=7x\\\\\Rightarrow x=(14)/(7)\\\\\Rightarrow x=2.$

So, from equation (iii), we get

Thus, the required solution of the given system is (x, y) = (2, 5).

Option (C) is CORRECT.