Question 358073
Let x = the large number
Let y = the small number
:
Write an equation for each statement:
:
Twice the small number is 5 more than 2/3 the larger number.
2y = {{{2/3}}}x + 5
Get rid of that annoying fraction, multiply by 3, results:
6y = 2x + 15
-2x + 6y = 15
:
 Three times the larger number is 4 less than 15 times the smaller number.
3x = 15y - 4
3x - 15y = -4
:
Use elimination here, multiply the 1st equation by 3, and the 2nd equation by 2
-6x + 18y = 45
+6x - 20y = -8
-------------------adding eliminates x, find y
-12y = 37
y = {{{-37/12}}}
:
Use the 1st equation to find x
-2x + 6({{{-37/12}}}) = 15
-2x + {{{-37/2}}}) = 15
Multiply by 2
-4x - 37 = 30
-4x = 30 + 37
-4x = 67
x = {{{-67/4}}}
:
A couple nasty fractions, see if they work in the 2nd equation
3x - 15y = -4
Substitute
3({{{-67/4}}}) - 15({{{-37/12}}} = -4
{{{-201/4}}} + ({{{555/12}}} = -4
multiply by 12 to get rid of those annoying fractions
3(201) + 555 = -48
-603 + 555 = -48; it does work, amazing isn't it!