Question

Find the greatest solution to the following system of equations. Write as x= ?

y=x^2+x-2 and y=-x+1

Answer 1

we have x=1, y=0 and x=-3, y=4

Explanation:

We need to solve the equations:
`y=x^2+x-2 \ and \ y=-x+1`

Let:

`y=x^2+x-2--eq(1)\\ y=-x+1---eq(2)`

Putting value of eq(2) into eq(1)

`-x+1=x^2+x-2\\Solving:\\x^2+x-2+x-1=0\\x^2+2x-3=0\\Factorising:\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x-1)(x+3)=0\\x-1=0 \ or \ x+3=0\\x=1 \ or \ x=-3`

Now finding values of y for x=1 and x=-3

`For \ x=1, \\y=-x+1 \\y=-1+1 \\y=0\\For \ x=-3\\ y=-x+1\\y=-(-3)+1 \\y=3+1\\y=4`

So, we have x=1, y=0 and x=-3, y=4