Here is another addition method question!!!?

Question

The equations are x + y = 13 and 22x + 36y = 356. I came up with the following answers y= -46 and x= 59 well for the second equation -46 does not work. Please help and show work so I can see where I messed up at.

Thanks again, this is so cool that I can ask people for help and get great results!

Answer 1

First: get rid of the "x" or "y" variable, let's get rid of y and solve for "x" > take the first coefficient (1) beside "y" in the first equation and multiply it by everything in the second equation. Take the second coefficient (36) beside the "y" in the second equation and multiply it by everything in the first equation. Since, 1 and 36 are positive, one has to be negative when multiplied.

-36(1x + 1y) = 13
1(22x + 36y = 356)
------------------------
+ -36x - 36y = -468
22x + 36y = 356
------------------------
- 14x = -112
- 14x/-14 = 112/-14
x = 8

Take the value of x = 8 and replace it with "x" in the first original equation:

8 + y = 13
8 - 8 + y = 13 - 8
y = 5

*Using the substitution method is better! Mark G used it- responded after me.

Answer 2

Rearrange the first equation x+y = 13 for x.

x = (13-y)

With the Second Equation 22x + 36y = 356 substitute the x using the first equation
(the * means multiply)

22(13-y) +36y = 356

Now simplify 22(13-y) by multiplying each item in the parenthesis by 22
22*13 =286
22*y = 22y

286 - 22y + 36y = 356

Simplify and Solve for y

36y - 22y = 356 - 286

14y = 70
divide both sides by 14
y = 70/14

y = 5

Substitute the value for y back into the firsl equation and solve for x

x + y = 13 becomes x + 5 = 13

x = 13 - 5

x = 8


Check your answer using the second equation

(22 * 8 ) + (36 * 5) = 356

176 + 180 = 356

356 = 356

Answer 3

Let's multiply the top eqn by 22. Then our system becomes
22x + 22y = 286
22x + 36y = 356
Subtracting, we get
14y = 70
So y = 5 and x = 8.
Check:
Obviously x + y = 13,
and 22x + 36y = 176 + 180 =356.

Answer 4

{x+y = 13
{22x + 36y = 356

Okay, multiply the first equation by -22 and add the two equations together to get rid of x.

and you get

14y = 70

so y = 5

then use any of the equations, substituting y = 5 to get x

so

x + 5 = 13
x = 8

Voila!

Answer 5

Multiply first rquation by -22

-22x - 22y = -286

Add with other eq.

14y = 70

y = 5

Plug into equation to solve for x

x + 5 = 13

x = 8

x = 8, y = 5

Answer 6

x+y=13
22x+22y=286
22x+36y=356
subtracting
14y=70
y=5
substituting
x=8
the solution set is {8,5}