9514 1404 393
Answer:
31. (x, y) = (-4, 4)
32. (x, y) = (1/6, 1/5)
Step-by-step explanation:
My preferred method is using a graphing calculator. The results are attached.
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32.
For systems without integer solutions, it can work well to use the "cross multiplication method." For that we write the equations in general form. I prefer integer coefficients, so we need to multiply the equations in problem 32 by 5 and 10, respectively.
30x -40y +3 = 0
30x +20y -9 = 0
Then the solutions are ...
x = ((-40)(-9) -(20)(3))/(30(20) -30(-40)) = 300/1800 = 1/6
y = ((3(30) -(-9)(30))/1800 = 360/1800 = 1/5
The solution is (x, y) = (1/6, 1/5).
Please note that this method is substantially identical to the use of Cramer's Rule. The denominators in the expressions for x and y are identical. They are the determinant of the coefficient matrix.
