Trouble with a simultaneous equation?????????

Question

it says solve the simultaneous question
x^2-6xy+y^2=17
x+3y+1=0
plz show workings out and the method you used to work out the equation as it would help a lot as it would give me a greater understanding

Answer 1

Solve the second equation for x in terms of y:

x = -(3y + 1)

(You could also solve for y in terms of x, but this form is simpler. No fractions.)

Substitute this for x in the first equation, expand and combine like terms. You will end up with a quadratic equation for y. Solve this quadratic. You should get y = -1 and y = 4/7.

Then take each of these and plug it into the equation

x = -(3y + 1)

to find the corresponding x value.