Question

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2 ​

Answer 1

Answer:

  substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

  x = 6y -8

  7(6y -8) -y = -2 . . . . . x variable eliminated

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The second equation is easily solved for y, so you could substitute that into the first equation.

  y = 7x +2

  -x +6(7x +2) = 8 . . . . . y-variable eliminated

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The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

   7(-x +6y) +(7x -y) = 7(8) +(-2)

  42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

  (-x +6y) +6(7x -y) = (8) +6(-2)

  -x +42x = -4 . . . . . . . . y-variable eliminated

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It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).