Answer: To solve this system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the equations. To do this, we will multiply the first equation by 3 and the second equation by 2, then add the two equations together:
(3x - 2y = 7) x 3 -> 9x - 6y = 21
(-3x + 5y = 5) x 2 -> -6x + 10y = 10
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3y = 31
Now that we have eliminated the variable x, we can solve for y by dividing both sides by 3:
y = 31/3
Next, we can use this value of y to solve for x in either of the original equations. Let's use the first equation:
3x - 2y = 7
3x - 2(31/3) = 7
3x - 62/3 = 7
3x = 7 + 62/3
3x = 83/3
Finally, we can solve for x by dividing both sides by 3:
x = 83/9
Therefore, the solution to the system of equations 3x-2y=7 and -3x+5y=5 is x = 83/9 and y = 31/3.