SOLUTION: Question: x²+y²=13 2x+y=1 I then tried to solve by substitution: y=1-2x x²+(1-2x)²=13 I then got a bit muddled up and wasn't sure how to expand (1-2x)² But the ans

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Question: x²+y²=13 2x+y=1 I then tried to solve by substitution: y=1-2x x²+(1-2x)²=13 I then got a bit muddled up and wasn't sure how to expand (1-2x)² But the ans      Log On


   

Question 12429: Question:
x²+y²=13
2x+y=1
I then tried to solve by substitution:
y=1-2x
x²+(1-2x)²=13
I then got a bit muddled up and wasn't sure how to expand (1-2x)²
But the answer i got would not factorise into two brackets so i decided to use the quadratic formula:
-b+/- sqrt ......
but this did not get the correct answer of:
x=-1.2, y=3.4
x=2, y=-3
Please help me because i don't have a clue what to do next!
Found 2 solutions by rapaljer, AnlytcPhil:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
What you did so far, looks right so far. Let's expand the square of the binomial:

y=1-2x
x²+(1-2x)²=13
x%5E2+%2B+1+-+4x+%2B+4x%5E2+=+13
5x%5E2+-+4x+-+12=+0
By quadratic formula
x+=+%284+%2B-+sqrt%2816-4%2A5%2A%28-12%29%29%29%2F%282%2A5%29
x+=+%284+%2B-+sqrt%2816%2B240%29%29%2F10
x+=+%284+%2B-+sqrt%28256%29%29%2F10

This is the square root of a perfect square, which means that the original equation DOES factor, and the quadratic formula was not necessary in this case. However, you are almost there now, so might as well finish it.
x=+%284+%2B-+16%29%2F10

x=+%284%2B16%29%2F10+=+20%2F10+=+2
x=+%284-16%29%2F10+=+%28-12%29%2F10+=+%28-6%29%2F5

Then solve for y using y = 1-2x
If x= 2, y = 1-2*2= -3

If x+=+-6%2F5, then y+=+1+-+2%2A%28%28-6%29%2F5%29= 1%2B+12%2F5 = 17%2F5

Points of solution would be (2,-3) and (++%28-6%29%2F5, 17%2F5 ).

Check for errors in my work!! Let me know if I made any.

R^2 at SCC

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
x²+y²=13
2x+y=1
I then tried to solve by substitution:
y=1-2x
x²+(1-2x)²=13
I then got a bit muddled up and wasn't sure how to expand
(1-2x)²
-----------
Then you went astray. To expand (1-2x)², write it as
(1-2x) multiplied by itself:
`
(1-2x)² = (1-2x)(1-2x)
`
Now use "FOIL" on that. You'll eventually end up with a quadratic
equation which can be solved by factoring. You'll get two answers
for x, and then you'll substitute each of these into y=1-2x to get
the corresponding values for y.
`
If you still have trouble
post again. I'll give you the answers:
`
There are two solutions
`
(2, -3) and (-6/5, 17/5)
`
Edwin