Question

Determine the number of solutions of the system y=-x-13x^2+2y=4

Answer 1

`\begin{gathered} y=x-1 \\ 3x^2+2y=4 \end{gathered}`

we can replace y on the second equation to find x

`\begin{gathered} 3x^2+2(x-1)=4 \\ 3x^2+2x-2=4 \\ 3x^2+2x-6=0 \end{gathered}`

to find X we need to use this formula to factor

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where a=3, b=2 and c=-6

so, replace

`\begin{gathered} x=\frac{-(2)\pm\sqrt[]{(2)^2-4(3)(-6)}}{2(3)} \\ \\ x=\frac{-2\pm\sqrt[]{4+72}}{6} \\ \\ x=\frac{-2\pm\sqrt[]{76}}{6} \\ \\ x=\frac{-1\pm\sqrt[]{19}}{3} \end{gathered}`

we have 2 solutions for x