First, since both of the equations are equal to y you can set the equations equal to each other.
y=-2x +1
y=-2x^2 + 3x +1
-2x + 1= -2x^2 + 3x + 1
Second, add 2x^2 and subtract 3x and 1 from both sides.
-2x + 1 = -2x^2 + 3x + 1
-3x -1 +2x^2 +2x^2 -3x -1
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2x^2 - 5x = 0
Third, factor out an x.
x(2x - 5) = 0
Fourth, solve for x by setting each factor equal to 0.
x= 0 2x-5=0
+5 +5
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2x = 5
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2 2
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x=5/2
So the values of x that satisfy the system of equations is 0 and 5/2.