What values of x and y satisfy `-(13)/(3)x −2y = 7` and `3x + (2)/(5) y = 5` simultaneously? a.  x  = 3 and  y  = −10b.  x  = −3 and  y  = −3c.  x  = 1 and  y  = 5d.  x  = 3 and  y  = 10

A graph quickly shows the solution to be ...

... A. x=3 and y=-10

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There are a couple of different strategies you can employ to eliminate possibilities.

1. Since the equations involve fractions, you can look only at answers that deal well with the fractions. That is, look for x-values that are multiples of 3 and y-values that are multiples of 5. Right away, this suggests you are not interested in choices B and C.

2. You can look at the general nature of the equations to see where the lines lie on a graph. It can be handy to know that intercept form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively. That is, you can divide by the constant on the right (or just pay attention to its sign) to check the signs of the intercepts. For the first equation, the intercepts are both negative. Hence there cannot be any 1st-quadrant solutions. (That line never goes through the first quadrant—eliminating choices C and D.)

Likewise, the intercepts for the second equation are both positive, so it will never go through the third quadrant—eliminating choice B.

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answer: d.) the total number of protons and neutrons is 15

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