What are the points of intersection?

Question

x^2 - 2X - Y=-2 
-3X+y=-2

Answer 1

The system of equations are x² - 2x - y  = -2 and - 3x + y  = - 2

Convert the two equations in y  form.

Then the equations are y  = x² - 2x + 2  and y  = 3x - 2.

Equate the two equations.

x² - 2x + 2 = 3x - 2

x² - 2x + 2 - 3x + 2 = 0

x² - 5x + 4 = 0

x² - 4x - x + 4 = 0

x (x - 4) - 1( x - 4) = 0

(x - 4)(x - 1) = 0

x - 1 = 0 and x - 4 = 0

x = 1 and x = 4

• Substitute x  values in either of two equations.

Substitute x  = 1 in - 3x + y  = - 2.

- 3(1) + y  = - 2

- 3 + y  = - 2

y  = 1

Substitute x = 4 in - 3x + y = - 2.

- 3(4) + y  = - 2

- 12 + y = - 2

y  = 10

The intersection points are (1, 1) and (4, 10).