Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair.

x – 3y = –23
5x + 6y = 74

A. (7, 12)
B. (4, 9)
C. (4, 7)
D. (7, 10)

Answer 1

B. (4, 9)

Multiply the top equation by 2 and the y values will eliminate. You can then solve for x. Plug that in to either equation afterwards to find y.

Answer 2

Answer: The correct option is (B) (4, 9).

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

`x-3y=-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\5x+6y=74~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

Multiplying equation (i) by 2, we have

`2(x-3y)=2* (-23)\\\\\Rightarrow 2x-6y=-46~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Adding equations (ii) and (iii), we get

`(5x+6y)+(2x-6y)=74-46\\\\\Rightarrow 7x=28\\\\\Rightarrow x=(28)/(7)\\\\\Rightarrow x=4.`

From equation (i), we again get

`x-3y=-23\\\\\Rightarrow 4-3y=-23\\\\\Rightarrow 3y=4+23\\\\\Rightarrow 3y=27\\\\\Rightarrow y=(27)/(3)\\\\\Rightarrow y=9.`

Thus, the required solution of the given system is (x, y) = (4, 9).

Option (B) is CORRECT.