# geometry

posted by .

how to solve
y= (x-2)^2+4
4x+2y=14
algebraically

• geometry -

By substitution:
y= (x-2)^2+4 ....(1)
4x+2y=14 ....(2)
Solve for y from (2) divided by 2:
2x+y=7
y=7-2x ...(2a)

Substitute (2a) in (1)
7-2x = (x-2)^2+4
Expand
7-2x = x^2-4x+4+4
x^2 -2x +1 = 0 ....(1a)

Solve 1(a) to get:
x=1 (duplicity 2)

Now substitute x=1 in (2a) to get
y=5

Substitute x=1,y=5 in (1) to check:
(1-2)^2+4 = 5 OK.

## Similar Questions

1. ### Algebra 2

How do I do this f(x) = x - 5 (x + 4)^(1/2) when f(x) = -5 I know I can just guess and chekc but I want to know how to do this algebraically by subsituting in -5 and trying to solve for x which I don't know how to do... so -5 = x - …
2. ### pre-cal

How do I find the domain of the following function algebraically?
3. ### Geometry

How do solve the equations algebraically?
4. ### solve algebraically

y=2x+6 x^2+y^2=8
5. ### Algebra

Solve each inequality algebraically:how do I solve this problem?
6. ### Math

We have an important chemsitry test due and I want to make sure that I do not mess up on my algebra. I am dealing with the integrated rate law, but my question is purely algebraically in nature. I hope, somebody can help me. 1) ln(A) …
7. ### Math Gr 12

We are learning to solve Factorable Polynomial Inequalities Algebraically. Question: Solve using intervals. (4x +1)(2-x) is greater than or equal to 0.
8. ### pre-calculus 11

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight line …
9. ### pre-calculus 11

I am asked to solve the absolute value equation of |1/2x +1| =x+1 graphically. I can solve this algebraically and consider two cases for the absolute value one being positive and the other negative. I know this will be a straight line …
10. ### Pre Calculas

7. For the function defined by: f(x)= {x^2, x<=1} {2x+1, x>1} a. evaluate f(0) 8. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices. 3x-y=0 5x+2y=22 9. Solve the …

More Similar Questions