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Look at the simultaneous equations below.

x - 6y = 10
3y^2 = 4x+7

a) show that 3y^2 -24y - 47 = 0
b) use part a) to solve the simultaneous equations. If any of your answers are decimals, give them to 1 d.p.

It’s asking for two possibilities of x and y - someone please help!

Look at the simultaneous equations below x 6y 10 3y2 4x7 a show that 3y2 24y 47 0 b use part a to solve the simultaneous equations If any of your answers are de class=


Answer :

sqdancefan

Answer:

  (x, y) = (0.2, -1.6) or (67.8, 9.6)

Step-by-step explanation:

You want the solution to the system of equations ...

  • x -6y = 10
  • 3y² = 4x +7

using substitution for x.

a) Substitution

The first equation can be used to write an expression for x:

  x = 6y +10 . . . . . . add 6y to both sides

This can be substituted for x in the second equation:

  3y² = 4(6y +10) +7

  3y² = 24y +40 +7

  3y² -24y -47 = 0 . . . . . . . subtract (24y+47) to get standard form

b) Solution

We can use the quadratic formula to solve this equation:

  [tex]y=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-24)\pm\sqrt{(-24)^2-4(3)(-47)}}{2\cdot3}\\\\y=\dfrac{24\pm\sqrt{24^2+12\cdot47}}{6}\approx\{9.6,-1.6\}[/tex]

Then x can be found from the equation above as ...

  x = 6y +10 = 34 ± √1140 ≈ {67.8, 0.2}

The solutions are (x, y) = (0.2, -1.6) or (67.8, 9.6).

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