Mathematics: 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)

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Use the substitution method to solve the system of

brylove5490

11.03.2022

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

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

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

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

So, from equation (iii), we get

$y=9-2\times2=9-4=5.$

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

Option (C) is CORRECT.

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