Help solve additon method/system. What do you do with the 2 variables?

Question

x +y=13

22x + 36y=356

Answer 1

elimination by addition method

x + y = 13- - - - - - - - -Equation 1
22x + 36y = 356- - - -Equation 2
- - - - - - - - - - - -

Multiply equation 1 by - 22

x + y = 13

- 22(x) + - 22(y) = - 22(13)

-22x + ( - 22y) = - 286

Remove parenthesis

- 22x - 22y = - 286

- - - - - - - - - - - - -

Elimination of x

- 22x - 22y = - 286
22x + 36y = 356
- - - - - - - - - - - - -
14y = 70

Divide both sides of the equation by 14

14y / 14 = 70 / 14

y = 70 / 14

y = 5

Insert the y value into equation 1
- - - - - - - - - -

x + y = 13

x + 5 = 13

Transpose 5

x + 5 - 5 = 13 - 5

x = 8

Insert the x value into equation 1

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Check for equation 1

x + y = 13

8 + 5 = 13

13 = 13

- - - - - - - - -

Check for equation 2

22x + 35y = 356

22(8) + 35(5) = 356

176 + 180 = 356

356 = 356
- - - - - - - - -

Both equations balance

The solution set { 8, 5 }

- - - - - - - - -s-

Answer 2

Using the addition method-
Note that 22x + 36y = 356 can be divided by 2 to get
11x + 18y = 178

the 2 equations-
x + y = 13
11x + 18y = 178

if you multiply the 1st equation by a minus 11 (-11) you will be able to add the two equations and eliminate the variable x-

-11x + (-11y) = -143
+11x + 18y = 178 ;addition yields-
0x + 7y = 35 ; so-
y = 5

Since y = 5, substitute 5 for y in the original equation to get-
x + 5 = 13 so x = 8

Answer 3

There are a few ways to do it. I will show you the "substitution" method:

Using the 1st eqn, solve for x:
x = 13-y

Now using the 2nd eqn, substitute for 'x':

22(13-y) + 36y = 356
286 - 22y + 36y = 356
14y = 70
y = 5

Now take this and substitute back in to the 1st original eqn:

x + 5 = 13
x = 8.
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The other method I will show you is the "elimination" method.
The idea here is to add the two eqns together and eliminate one of the variables. First, we need the coefficients to match negatively so when we add them, one variable cancels. So, we'll multiply the 1st eqn by -22:

-22x - 22y = -286
+22x+36y=356
-----------------------
14y = 70 --- notice we end up with the same eqn as we did with "substitution" method

y = 5.

Plug 5 back in to the 1st eqn:

x + 5 = 13
x = 8.

Answer 4

x+y=13____(1)
22x+36y=356___(2)
you must either,
multiply x+y =13 by 22 or 36

if (1) multiplied by 22
then
22x+22y=286_____(3)
(2)-(3)
22x+36y-22x-22y=356-286
14y=70
y=1/5 or 0.2
and using the value of y in (1),
x+0.2=13
x=13-0.2
x=12.8