Question

The answer the book gave was (1/2, -2)

Answer 1

Answer:

  (x, y) = (1/2, -2)

Step-by-step explanation:

Many people find it convenient to work these problems by eliminating fractions as a first step.

Here, you can do that by multiplying the first equation by 4

  4(1/2x +2y) = 4(-15/4)

  2x +8y = -15

From here, there are a number of possibilities for arriving at a solution.

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Multiply the first equation by 2 and you have ...

  4x +16y = -30

The second equation says you can replace the first term with -y:

  -y +16y = -30

  15y = -30

  y = -30/15 = -2

Substituting this value into the second equation gives ...

  4x = -(-2) = 2

  x = 2/4 = 1/2

The solution is (x, y) = (1/2, -2).

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Alternate solution

You can rearrange the second equation to give an expression for y:

  y = -4x

Then, substitute this into the first equation:

  (1/2)x +2(-4x) = -15/4

  (-15/2)x = -15/4

  x = (-15/4)/(-15/2) = 2/4 . . . . . . divide by the coefficient of x

  x = 1/2

  4(1/2) = -y = 2 . . . . . substitute for x in the second equation

  y = -2 . . . . . . . . . . . . multiply by -1

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Additional comments on problem solving

I find the key to working troubling problems is to be very meticulous. Make certain you follow the rules of algebra: anything you do to one side of the equation must also be done to the other side. I find it easier to think in those terms when moving stuff around.

Some folks would say, "move this term over there and ...". I like to think of it as "subtract this term from both sides of the equation."

It also helps to be careful when dealing with fractions. Make sure you know how to add, subtract, multiply, and divide fractions. You should be just as able to handle that arithmetic as with integers or decimals. Use a calculator if your skills are shaky.

As you may notice, a graphing calculator can help you verify your answer.