solve the following system of equations algebraically:?

Question

y=x^2-6x+6
y-x=-4

y=x*2-6x+6, y-x=-4

Answer 1

y - x = -4

add x for both sides
y = x - 4

y=x^2-6x+6
y = x - 4

subtract the equations
0 = x^2 - 7x + 10

factor
0 = (x - 2) (x - 5)

x = 2 or 5

y = x - 4
y = 2 - 4
y = -2

y = 5 - 4
y = 1

so the solutions are:
(5,1) and (2, -2)

Answer 2

two equations and two unknowns can be solved by substitution.

Use the second equation for the substition, set the second equation equal to y (it's easier to substitue for y then for x).

So the second equation looks like y=x+4

No plug that into the first equation so it no looks like this:

x-4=x^2-6x+6

Set that equation equal to zero: 0=x^2-7x+10

Now use the quadratic formula to slove for x:
x= [-b+sqrt(b^2-4ac)]/(2a) and x= [-b-sqrt(b^2-4ac)]/(2a)
where a=1 b=-7 and c=10

Note if the number under the radical is negative then you have imaginary or complex zero's--ie sqrt(-4)=2sqrt(-1)=2i which usually DO NOT COUNT!!!

Now after you found all the real values of x plug in that value into the second equation: y=x-4

Answer 3

y = x - 4

substitute y in eq 1

x-4 = x^2 - 6x + 6
x^2 - 7x + 10 = 0
(x - 5)(x - 2)= 0

x = 5, or 2

Answer 4

y = x^2 - 6x + 6
y - x = -4

y = x - 4

x - 4 = x^2 - 6x + 6

x^2 - 7x + 10 = 0

(x-2)(x-5) = 0

x=2 and x=5

y-2 = -4
y = -2

y-5 = -4
y=1

(2,-2) (5,1)

Answer 5

y=x^2-6x+6
y-x=-4
so in the second equations
y=x-4 also
you can plug this in for y in the other equation
x-4=x^2-6x+6
simplify
x^2-7x+10=0
then you solve the equation
with (x-5)(x-2)=0
so x=5,2
then you plug this back to get y
y-5=-4
y=1
the other equation
y-2=-4
y=-2

Answer 6

x² - 6x + 6 = x - 4
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
x = 2 , x = 5
y = - 2 , y = 1

(2 , - 2) , (5 , 1)

Answer 7

9x² + y² = 9 3x - y = 3 - y = 3 - 3x y = - 3 + 3x, or y = 3x - 3 9x² + (3x - 3)² = 9 9x² + 9x² - 9x - 9x + 9 = 9 18x² - 18x + 9 - 9 = 0 18x² - 18x = 0 18x(x - a million) = 0 18x = 0 x = 0 x - a million = 0 x = a million x{0, a million) y = 3x - 3.....(From above) y = 3(0) - 3 y = - 3 y = 3(a million) - 3 y = 3 - 3 y = 0 y{- 3, 0} answer set (0, - 3) U (a million, 0) ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Answer 8

(x^2-6x+6)-x=-4
x^2-7x+10=0
(x-5)(x-2)=0
x=5 & 2

y-5=-4
y=1

y-2=-4
y=-2

Answer 9

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