Question

To solve the system of linear equations 8 x + 5 y = 18 and 6 x + y = negative 2. by using the linear combination method, Amos decided that he should first multiply the second equation by –5 and then add the two equations together to eliminate the y-terms. His calculations are as shown. 8 x + 5 y = 18. + 6 x minus 5 y = 10. 14 x = 28. StartFraction 14 x Over 14 EndFraction = StartFraction 28 Over 14 EndFraction. X = 2. 6 x + y = negative 2. 6 (2) + y = negative 2. 12 + y = negative 2. 12 + y minus 12 = negative 2 minus 12. y = negative 14. Amos’s solution is (2, –14). What did he do wrong? He multiplied the equation 6 x + y = negative 2. by –5 incorrectly. He added the equations 8 x + 5 y = 18 and 8 x + 5 y = 18 incorrectly. He substituted 2 into the equation 6 x + y = negative 2. incorrectly. He solved the equation 12 + y = negative 2 for y incorrectly.

Answer 1

(A)He multiplied the equation
`6x+ y = - 2` by –5 incorrectly.

Explanation:

To solve the system of linear equations:

• 8 x + 5 y = 18

• 6 x + y = -2.

Part of Amos' calculations is shown:

8 x + 5 y = 18.

6 x -5 y = 10.

When you multiply 6x+y =-2 by -5, we have the expression:

• -30y-5y=10.

This was not Amos' result as he got 6 x -5 y = 10.

Therefore, he multiplied the equation
`6x+ y = - 2` by –5 incorrectly.

The correct option is A.