At which points are the equations y = x2 + 5x − 2 and y = x + 1 equal?

When they are equal, y=y, so we can say:

x^2+5x-2=x+1  subtract x from both side

x^2+4x-2=1  add 2 to both sides

x^2+4x=3, now add half the linear coefficient squared, (4/2)^2=4

x^2+4x+4=3+4 now the left side is a perfect square

(x+2)^2=7  now take the square root of both sides

x+2=±√7  subtract 2 from both sides

x=-2±√7

x=-2+√7 and -2-√7

y=x+1 the two points where these equations are equal are:

(-2-√7, -1-√7) and (-2+√7, -1+√7)

or approximately:

(-4.65, -3.65) and (0.65, 1.65)

Step-by-step explanation:

corresponding angles- 4 and 2, 12 and 10, 5 and 7, 13 and 15

alternate interior-  3 and 7,6 and 2, 11 and 15, 14 and 10

alternate exterior - 4 and 8, 5 and 1, 13 and 9, 12 and 16

consecutive interior angles - 3 and 2, 6 and 7, 11 and 10 , 14 and 15

Step-by-step explanation: