Answer:
 A-2, B-DNE*, C-3, D-DNE, E-4, F-1
Step-by-step explanation:
The first attachment shows the solutions to A and C.
The second attachment shows the solutions to E and F.
There are no real number solutions to systems B and D.
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In general, you can solve the linear equation for y, then substitute that into the quadratic. You can subtract the x-term on the left and complete the square to find the solutions.
A.
 (3-x) +12 = x^2 +x
 15 = x^2 + 2x
 16 = x^2 +2x +1 = (x +1)^2 . . . . add the square of half the x-coefficient to complete the square; next take the square root
 ±4 -1 = x = {-5, 3) . . . . . identifies the second solution set for system A
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B.
 (x -1) -15 = x^2 +4x
 -16 = x^2 +3x
 -13.75 = x^2 +3x +2.25 = (x +1.5)^2
roots are complex: -1.5 ±i√13.75
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C.
 (1-2x) +5 = x^2 -3x
 6 = x^2 -x
 6.25 = x^2 -x + .25 = (x -.5)^2
 ±2.5 +.5 = x = {-2, 3} . . . . . identifies the third solution set for system C
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remaining problems are done in a similar way.
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* DNE = does not exist. There is no matching solution set for the complex numbers that are the solutions to this.
