Question 1173233
let x = your age.
let y = your sister's age.


5 times your age plus 2 times your sister's age = 64
the equation for that is 5x + 2y = 64


3 times her age minus 2 times your age = 1
the equation for that is 3y - 2x = 1


solve for x in the first equation as shown below.
start with 5x + 2y = 64.
subtract 2y from both sides of the equation to get:
5x = 64 - 2y
divide both sides of the equation by 5 to get:
x = (64 - 2y) / 5


replace x in the second equation with this to get:
3y - 2x = 1 becomes:
3y - 2 * (64 - 2y) / 5 = 1
multiply both sides of this equation by 5 to get:
15y - 2 * (64 - 2y) = 5
simplify to get:
15y - 128 + 4y = 5
combine like terms to get:
19y - 128 = 5
add 237 to both sides of this equation to get:
19y = 133
solve for y to get:
y = 133/19 = 7


replace y with 7 in the equation of 5x + 2y = 64 to get:
5x + 14 = 64
subtract 14 from both sides of the equation to get:
5x = 50
solve for x to get:
x = 50/5 = 10


you have x = 10 and y = 7


confirm by replacing x and y in both original equations to get:
5x + 2y = 64 becomes 5 * 10 + 2 * 7 = 64 which becomes 50 + 14 = 64 which becomes 64 = 64 which is true.
3y - 2x = 1 becomes 3 * 7 - 2 * 10 = 1 which becomes 21 - 20 = 1 which becomes 1 = 1 which is true.


you were 10 years old and she was 7 years old this year.


your solution is that you were 9 years old and she was 6 years old last year.