In each case, you can use the second equation to create an expression for y that will substitute into the first equation. Then you can write the result in standard form and use any of several means to find the number of solutions.
System A x² + (-x/2)² = 17 x² = 17/(5/4) = 13.6 x = ±√13.6 . . . . 2 real solutions
System B -6x +5 = x² -7x +10 x² -x +5 = 0 The discriminant is ... D = (-1)²-4(1)(5) = -20 . . . . 0 real solutions
System C y = 8x +17 = -2x² +9 2x² +8x +8 = 0 2(x+2)² = 0 x = -2 . . . . 1 real solution
