Question

Find the solutions to the system of equations. y = x2 - 1y = 2x - 2

Answer 1

Write out the two equations

`\begin{gathered} y=x^2-1-----\text{eqn}(1) \\ y=2x-2-----\text{eqn}(2) \end{gathered}`

Since y=y, then equate the two equations

`\begin{gathered} \text{since y=y,} \\ x^2-1=2x-2 \\ x^2+2x-1+2=0 \\ x^2+2x+1=0 \\ x^2+x+x+1=0 \\ x(x+1)+1(x+1)=0 \\ (x+1)(x+1)=0 \end{gathered}`
`\begin{gathered} (x+1)^2=0 \\ x+1=0 \\ x=-1 \\ \text{Hence, x=-1 twice} \end{gathered}`

Substitute x=-1 in equation 1

`\begin{gathered} y=x^2-1 \\ y=(-1)^2-1 \\ y=1-1 \\ y=0 \end{gathered}`

Hence, the solutions to the system is x=-1, y=0 i.e. (-1,0)