Question

To solve the system of linear equations 8x+5y=18 and 6x+y=-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.

Amos’s solution is (2, –14). What did he do wrong?
He multiplied the equation 6x+y=-2 by –5 incorrectly.
He added the equations 8x+5y=18 and 6x+y=-2 incorrectly.
He substituted 2 into the equation 6x+y=-2 incorrectly.
He solved the equation 12+y=-2 for y incorrectly.

Answer 1

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

Step-by-step explanation:

We are given the following in the question:

Steps to solve the equation are given by Aman.

The equations are:

$8x+5y=18\\6x+y=-2$

He multiplied the second equation by -5 and added them to eliminate y.

He incorrectly multiplied the equation by -5.

$-5\times (6x+y=-2)\\-30x - 5y = 10$

The step of multiplication was wrong which lead to further incorrect steps.

The correct solution for equation is:

$8x + 5y=18\\-30x - 5y = 10\\\text{Adding we get,}\\-22x = 28\\\\\Rightarrow x = \dfrac{-14}{11}\\\\\text{Putting this value in the equation}\\\\6\times \dfrac{-14}{11} + y = -2\\\\y = \dfrac{62}{11}$

Thus, he made a mistake in the first step of multiplication.

#LearnMore

After solving the linear equation -6x+5y=2 and -5x+6y=9, the value of y will be-

https://brainly.in/question/12655781

Answer 2

Answer:

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

Step-by-step explanation:

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