Use the elimination method to solve the system of equations. choose the correct ordered pair. x+y=8 x-y=6

Explanation:

Step-by-step x+y=8;x−y=6

Step: Solve x+y=8 for x:

x+y=8

x+y+−y=8+−y(Add -y to both sides)

x=−y+8

Step: Substitute−y+8 for x in x−y=6:

x−y=6

−y+8−y=6

−2y+8=6(Simplify both sides of the equation)

−2y+8+−8=6+−8(Add -8 to both sides)

−2y=−2

−2y

−2

=

−2

−2

(Divide both sides by -2)

y=1

Step: Substitute 1 for y in x=−y+8:

x=−y+8

x=−1+8

x=7(Simplify both sides of the equation)

x=7 and y=1

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7,1 apex

Step-by-step explanation:

add an image

step-by-step explanation:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!