Question

Given the system below:
f(x)=2x
g(x)=2x

Which value(s) of x make f(x)=g(x) a true statement? If necessary, you many choose more than one answer.
0
1
2
3
4

Answer 1

f(x) = g(x)

2x = 2x

what values can you use to keep that true,

Answer 2

you have two forms of the same line y=2x,
they overlap at infinite points, and have infinite solutions

Answer 3

1)

If f(x) = 2x and g(x) = 2x, then f(x) = g(x), since 2x = 2x. Therefore, f(x) = g(x) for all values of x, so all choices are correct (0, 1, 2, 3, 4).


2)

For this one, you want to solve for y for both equations (the first one is already done):

y = -x^2 - x + 2

x + y = -2
y = -x - 2


Now you can set both equations equal to each other:

y = y
-x^2 - x + 2 = -x - 2
-x^2 - x + x + 2 + 2 = 0
-x^2 + 4 = 0
-(x^2 - 4) = 0

x = -2, +2


To find the y-values, just plug x into either of the equations:

y = -x - 2
y = -(-2) - 2
y = 2 - 2
y = 0 when x = -2

y = -2 - 2
y = -4 when x = +2


Your answers are (-2, 0) and (2, -4)



3)

Solve this one using the exact same method as above:

y = (1/2)x^2 + 2x - 1

3x - y = 1
-y = -3x + 1
y = 3x - 1


(1/2)x^2 + 2x - 1 = 3x - 1
(1/2)x^2 + 2x - 3x -1 + 1 = 0
(1/2)x^2 - x = 0
x(1/2x - 1) = 0


Now set each factor equal to 0 and solve for x:

x = 0

(1/2)x - 1 = 0
(1/2)x = 1
x = 2


Plug x into either equation to get y:

y = 3(0) - 1
y = -1 when x = 0

y = 3(2) - 1
y = 6 - 1
y = 5 when x = 2


The answers are (0, -1) and (2, 5)

Answer 4

Ok thanks guys

Answer 5

Your welcome