simultaneous equation help Can someone help me with to solve this system of equations ?
$$
\left\{ 
\begin{array}{c} 
y=x+1 \\
y^2+2x^2=2
\end{array}
\right.
$$

We know from equation one that $y = x+1$. Plugging this value into equation two we get 
\begin{align*}
y^2+2x^2 &= (x+1)^2+2x^2 \\
&=x^2+2x+1+2x^2\\
&=3x^2+2x+1 \\
\end{align*}
We know that $3x^2+2x+1 = 2$ from equation two. Simplifying we get $$3x^2+2x-1 = 0$$$$(x+1)(3x-1) = 0 \tag{factoring}$$
$$x = -1, \frac{1}{3}$$Plugging in these values of $x$ into $y = x+1$ we get that $y=0, \dfrac43$ So the solutions are $$\boxed{\left(-1,0\right)\ \& \left(\frac13, \frac43\right)}$$
