Non linear eqs

Solve the system of non-linear equations:

3x²-3x-y=-2
-6x²-x-y=-7

Correct answer:

x₁ =  0.8647
y₁ =  1.649
x₂ =  -0.6425
y₂ =  5.1658

Step-by-step explanation:

$$\begin{gathered} 3x^2-3x-y=-2 \\ -6x^2-x-y=-7 \\ y=-6x^2-x+7 \\ 3x^2-3x-(-6x^2-x+7)=-2 \\ 3x^2-3x-(-6x^2-x+7)=-2 \\ 9x^2-2x-5=0 \\ a=9;b=-2;c=-5 \\ D=b^2-4ac=2^2-4\cdot 9\cdot (-5)=184 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{2\pm \sqrt{184}}{18}}={\displaystyle \frac{2\pm 2\sqrt{46}}{18}} \\ {x}_{1,2}=0.11111111\pm 0.753592220347 \\ {x}_1=0.864703331458 \\ {x}_2=-0.642481109236 \\ \text{ Factored form of the equation: } \\ 9(x-0.864703331458)(x+0.642481109236)=0 \\ {x}_1=0.8647 \end{gathered}$$

Our quadratic equation calculator calculates it.

$y_1=-6\cdot x_1^2-x_1+7=-6\cdot 0.8647^2-0.8647+7=1.649$

$x_2=(-0.6425)=-0.6425$

$y_2=-6\cdot x_2^2-x_2+7=-6\cdot (-0.6425{)}^2-(-0.6425)+7=5.1658$

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