Question 119871
Let the two numbers be x and y.
{{{x+y = 15}}} and...
{{{2x = 3y}}} rewrite this as: {{{x = (3/2)y}}} and substitute into the first equation.
{{{(3/2)y+y = 15}}} Combine like-terms.
{{{(5/2)y = 15}}} Multiply both sides by the multiplicative inverse of {{{5/2}}} which is {{{2/5}}}.
{{{y = 6}}}
{{{x = (3/2)y}}}
{{{x = (3/2)(6)}}}
{{{x = 9}}}
Check:
{{{x+y = 15}}} Substitute x = 9 and y = 6.
{{{9+6 = 15}}}
{{{15 = 15}}} OK, and...
{{{2x = 3y}}}
{{{2(9) = 3(6)}}}
{{{18 = 18}}} OK