Solve the system of equations y=3x.
y=x^2-4

  (x, y) = (-1, -3)  or  (4, 12)

Step-by-step explanation:

A graphing calculator can show the solutions to this system.

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You can equate expressions for y and solve for x.

  3x = x^2 -4

  x^2 -3x = 4 . . . . add 4-3x

  x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.

  (x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares

  x -1.5 = ±2.5 . . . . . . . . . . take the square root

  x = 1.5 ± 2.5 = -1, +4

  y = 3x = -3, +12, respectively

Solutions are ...

  (x, y) = (-1, -3) . . . . and . . . . (4, 12)

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15