Solve the following system of equations. enter the x-coordinate of the solution. round your answer to the nearest tenth
5x+2y=22
-2x+6y=3

The answer to your question is: x = 3.7

Step-by-step explanation:

                                              5x+2y=22          (1)

                                              - 2x+6y=3         (2)

Multiply (1) by -3

                                           -3  ( 5x+2y=22 ) = -15x -6y = -66

Solve by elimination

                                          -15x -6y = -66

                                          - 2x+6y=3

                                         - 17 x       = -63

                                               x = -63 / -17

                                              x = 3.7

                                     -2(3.7) + 6y = 3

                                    -7.4 + 6y = 3

                                              6y = 3 + 7.4

                                              6y = 10.4

                                                y = 1.7

x = 63/17 ≅ 3.7

y = 59/34 ≅ 1.7

Step-by-step explanation:

5*x+2*y=22  (1)

-2*x+6*y=3 (2)

First, isolate x in the first equation, to get

5*x=22 - 2*y

x = 22/5 - (2/5)*y (3)

Then, replace eq. 3 into eq. 2, as follows

-2*[22/5 - (2/5)*y] + 6*y = 3

-44/5 + (4/5)*y + 6*y = 3

(34/5)*y = 3 + 44/5

y = (59/5)*(5/34)

y = 59/34 ≅ 1.7

Replacing this value in eq.1, we get

5*x+2*(59/34) = 22

5*x = 22 - 59/17

x = (315/17)*(1/5)

x = 63/17 ≅ 3.7

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!