b- smaller number

a = b+10

2b+3a = 55

substitute

2b+3(b+10) = 55

distribute

2b+3b+30 = 55

Simplify

5b+30 = 55

Subtract 30 from both sides

5b = 25

b = 5

Substitute back into the first equation

a = b+10

a = 5+10

a= 15

small number = 5

larger number = 15

y= x+10

2x+3y =

2x+3(x+10) =

2x+3x+30 =

5x+30 =55

5x= 55-30=25

x= 25/5 =5

so y= x+10= 5+10=15

Larger – (x+10)

2(x) + 3(x + 10) = 55

2x + 3x + 30 = 55

5x = 25

x = 5

The first sentence tells you that

Y = X + 10

The second sentence tells you that:

2X+3Y = 55

You now have two equations in two unknowns. If you know linear algebram it is easy to solve.

If you don’t — then replace Y with (X+10) in the second equation. This gives you:

2X+3(X+10) = 55

or

2X+3X+30 = 55

or 5X + 30 = 55

You should be able to do the rest yourself.

x + 10 = second number

2x + 3(x + 10) = 55

5x + 30 = 55

5x = 25

x =5

x + 10 = 15