Question

Solve the system y = -x + 7 and y = -0.5(x - 3)2 + 8

Answer 1

how do i do this

Answer 2

There are several methods you may use. Substitution is a popular method and would be a good method because both equations equal y. Since y = y then the expressions to the right of the equal sign are also equal.

Answer 3

This being the case we now can write:

-x + 7 = -0.5(x - 3)2 + 8 In order to be sure I believe what is intended here is:
\[-x + 7 = -0.5(x - 3)^{2} + 8\]Is the case?

Answer 4

*Is this the case?

Answer 5

yes

Answer 6

Thank you for helping me.

Answer 7

O.K. Firs clear the parentheses on the right expression: You should get a result of....
-x + 7 = -0.5(x^2 - 6x + 9) + 8
Now multiply thru by 2 getting
-2x + 14 = -x^2 + 6x -9 + 16
Simplify the equation getting:
x^2 -8x + 7= 0
Now you have a quadratic equation that can be easily factored and solve giving two values for x.
Have you studied the solutions of quadratic equations yet?

Answer 8

Factor this quadratic equation getting:
(x - 7)(x - 1) = 0 Now solve getting:
x - 7 = 0, thereby x = 7 and
x - 1 = 0, thereby x = 1 two results, we are not thru, we got to solve for y. solve and verify by substituting these values in EACH of the original equations.

Answer 9

Verification:
y = -x + 7 for x = 1, y = -1 + 7 = 6 or (1,6)
y - -x + 7 for x = 7, y = -7 + 7 = 0 or (7,0)

Now for the critical test use the next original equation, if correct we will come out with same results.

Answer 10

-0.5(x - 3)2 + 8\[y = -0.5(1 - 3)^{2} + 8 =-0,5(-2)^{2}+8=-2+8=6\] (1,6) same as first equation good so far, but has to work out with x = 7.
\[y=-0.5(7 - 3)^{2} + 8 = -8 + 8 = 0\]Does indeed check out (7,0) x=7 y=0.
That is the solutions of that system X=1, Y=6 and X=7, Y=0

Answer 11

Did you follow, if not say where you went off the rail.

Answer 12

I will wait for your response before logging off.

Answer 13

i understand it all thank you again for helping me

Answer 14

You're welcome and good luck with your studies.