Solve y = 2-3x and y=x^2-2 graphically and algebraically. Verify the solution by substitution.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equations y=2-3x and y=x^2-2 have to be solved graphically and algebraically.

Graphically, this is done by plotting the graph of the two functions; the points of intersection are the solutions.

The points of intersection of the two graphs are (1, -1) and (-4, 14)

Solving the equations algebraically, substitute y = 2 - 3x in y = x^2 - 2

=> 2 - 3x = x^2 - 2

=> x^2 + 3x - 4 = 0

=> x^2 + 4x - x - 4 = 0

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

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

=> x = 1 and x = -4

For x = 1, y = -1 and for x = -4, y = 14

As a verification of the solution:

(1, -1): 2 - 3x = 2 - 3 = -1 and 1^2 - 2 = -1

(-4, 14): 2 - 3x = 2 + 12 = 14 and 16 - 2 = 14

The solution of the equations y=2-3x and y=x^2-2 is (1, -1) and (-4, 14)

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