Question

xavier is two years more than twice as old as Yoko. The sum of their ages is 86. How old are they

?

Answer 1

Xavier age = X
Yoko age = Y
Now translate the two equations:

first x = 2 + 2y

Answer 2

second if the two ages added together equal 86
the equation would be X + y = 86

Answer 3

that gives us x = 2 + 2y
x + y = 86
which is a system of equations
do you know how to solve a system of equations?

Answer 4

srry i dont remember havent done this in a while

Answer 5

need to make both equations look the same. lets change the 1st one so it has the x and y on the same side, by subtracting 2y on both sides
x = 2 + 2y
-2y - 2y
x - 2y = 2

Answer 6

now our two equations look like this

x - 2y = 2
x + y = 86

to solve this we need to eliminate either the x or y variable.
since the x's have the same coefficient, I am going to subtract them

Answer 7

x - 2y = 2
- x + y = 86

-3y = -84

y = 28

Answer 8

-2 + 1 is -1

Answer 9

once you know y = 28, substitute it in to eithr of the equations to find out what x equal.

x + 28 = 86, then solve for x

Answer 10

you are right, but remember we are subtracting....so it is -2 -1 = -3

Answer 11

ohh ok

Answer 12

but since the negative is applied to both wouldn't
the 2 become positive and the 1 negative

Answer 13

yes that is anothr way to look at it.

instead of subtracting, you could also multiply the bottom equation by the negative 1, then add the two equations togther. that would look like this

x - 2y = 2
-1) x + y = 84 if you are going to do it this way, remember to multiply the
negative 1 by everything on bottom equaiton

x - 2y = 2
-x - y = =-86 now instead of subtracting like I did, you would add

0 - 3y = -84

-3y = -84

Answer 14

is x -54

Answer 15

x + 28 = 86
- 28 -28
x = 58