What is the solution to the system of equations -6x-2/5y=8 1/2x+3y=29

10,-2
10,2
2,10
-2,10

x = -2 , y = 10 thus -2,10 is the answer

Step-by-step explanation:

Solve the following system:

{-6 x - (2 y)/5 = 8 | (equation 1)

x/2 + 3 y = 29 | (equation 2)

Add 1/12 × (equation 1) to equation 2:

{-(6 x) - (2 y)/5 = 8 | (equation 1)

0 x+(89 y)/30 = 89/3 | (equation 2)

Multiply equation 1 by 5/2:

{-(15 x) - y = 20 | (equation 1)

0 x+(89 y)/30 = 89/3 | (equation 2)

Multiply equation 2 by 30/89:

{-(15 x) - y = 20 | (equation 1)

0 x+y = 10 | (equation 2)

Add equation 2 to equation 1:

{-(15 x)+0 y = 30 | (equation 1)

0 x+y = 10 | (equation 2)

Divide equation 1 by -15:

{x+0 y = -2 | (equation 1)

0 x+y = 10 | (equation 2)

Collect results:

 {x = -2 , y = 10

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!

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )