Plz 20 ! i will give ! solve the system of linear equations below. y = -2x + 19 y = x + 7 a. x = 4, y = 11 b. x = -12, y = -5 c. x = -4, y = 3 d. x = 8, y = 3

A

Step-by-step explanation:

since both equations express y in terms of x we can equate the right sides

x + 7 = - 2x + 19 ( add 2x to both sides )

3x + 7 = 19 ( subtract 7 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

substitute x = 4 into either of the 2 equations for y

y = x + 7 ⇒ y = 4 + 7 = 11

solution is (4, 11 )

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!