SOLUTION: Solve by substitution {{{x^2+y^2=26}}} {{{y=-x+8}}}

Question 140321: Solve by substitution

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equations

Start with the first equation

Plug in

Foil

Subtract 26 from both sides

Combine like terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=2, b=-16, and c=38

Negate -16 to get 16

Square -16 to get 256 (note: remember when you square -16, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 2 to get 4

After simplifying, the quadratic has roots of

or

------------------------------------------

Answer:

Since we get a complex solution for the equation , this means that the equations and do not intersect. So there are no solutions
RELATED QUESTIONS
Solve by substitution. x-y=6 x=y+2 (answered by checkley77)

Solve by substitution {{{x^2+y^2=16}}} {{{x^2-2y=8}}} (answered by jim_thompson5910)

solve by the substitution method x+y+8... (answered by richwmiller)

Solve this system by Substitution. y = x^2 - 8 and 2x + y = 6 (answered by Timnewman,TeachMath)

solve by using substitution x+y=10... (answered by MathLover1)

solve by substitution x + 3y = 2 -x + y =... (answered by Marth)

Solve by substitution. x + 3y = 2 -x + y =... (answered by Alan3354)

Solve by substitution. x/2+y/3=-2... (answered by lynnlo)