We first solve the first line for y (so we can substitute):

`y=(x+6)/6`

Substituting in the second row gives:

`x^2+3((x+6)/6)^2=36`

Expand the brackets:

`x^2+3((x^2+12x+36)/36)=36`

Cancel the 3 and 36:

`x^2+((x^2+12x+36)/12)=36`

Multiply throughout by 12:

`12x^2+x^2+12x+36=432`

`13x^2+12x-396=0`

Solving using the quadratic formula gives:

`x = 5.077`, or `x = −6`

This gives us solutions of: `(5.077, 1.85)` and `(−6,0)`.

Graphically, we have:

1234567-1-2-3-4-5-6-712345-1-2-3-4xyOpen image in a new page

Graphs of `y = (x+6)/6` and `x^2+3y^2=36`: Intersection of line and ellipse

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