Question

For the solution (x,y) to the system of equations what is the value of x- y? 7x+3y=8 6x-3y=5

Answer 1

Answer:

  2/3

Step-by-step explanation:

Let's  define z = x-y, so solving for z will tell us exactly what we want to know. Then we can substitute for x: x = z+y, and our equations become ...

  7(z+y)+3y = 8   ⇒  7z +10y = 8

  6(z+y)-3y = 5   ⇒   6z +3y = 5

We can eliminate the y-variable by subtracting 3 times the first equation from 10 times the second:

  10(6z +3y) -3(7z +10y) = 10(5) -3(8)

  60z +30y -21z -30y = 50 -24 . . . . eliminate parentheses

  39z = 26 . . . . collect terms

  z = 26/39 = 2/3 . . . . . divide by the coefficient of z and reduce

The value of x - y is 2/3.

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The attached graph shows (x, y) = (1, 1/3), so x - y = 1 - 1/3 = 2/3.