If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the second equation is substituted into the
first equation.
2x – 3y = -29
x + 4y = 13 (6 points)
1) 2(4y + 13) – 3y = -29
2) 2(-4y + 13) – 3y = -29
3) 2x - 3(4y + 13) = -29
O4) 2x - 36-4y + 13) = -29

Option 2

Step-by-step explanation:

We will use the substitution method, as the question asks for. The second equation (where x or y is isolated on one side) will be susbstituted as the x or y in the first equation.

2x-3y=-29

x+4y=13

let's isolate x onto one side in the second equation.

Subtract 4y from both sides

x=-4y+13

now we can substitute the expression as x in the first equation

2(-4y+13)-3y=-29

it's the 2nd option

Hope this helps!

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!

they used 313 gallons of paint