Solve the system using elimination. SHOW ALL WORK on a separate sheet of paper.
52 - 2y = -48
2x + 3y = -23

y=50 and x=-173/2

Step-by-step explanation:

52-2y=-48

∴-2y=-100

y=50

and 2x+3y=-23

y=50→(1)

2x+3y=-23→(2)

Putting y=50 in equation (2), we get

⇒2x+3y=-23

⇒2x+3(50)=-23

⇒2x+150=-23

⇒2x=-23-150

⇒2x=-173

⇒x=-173/2

∴y=50 and x=-173/2

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!