Question 951875

Hi!! I am learning the substitution method with systems of equations and the elimination method!! how do I start solving this problem? 'Four times the larger of two numbers is equal to seven times the smaller. The sum of the numbers is 22. Find the numbers.' 

thanks!
<pre><b><u>Method 1: SUBSTITUTION</b></u>
Let larger number be L, and smaller, S. Then, we get: 
4L  = 7S ------- eq (i)
L + S = 22______L = 22 - S ------ eq (ii)
4(22 - S) = 7S ------- Substituting 22 - S for L in eq (i)
Continue to solve for S, or smaller number. Then substitute the value for S into any of the
2 original equation to determine the value of L, the larger number.

<b><u>Method 2: ELIMINATION</b></u>
Let larger number be L, and smaller, S. Then, we get: 
4L  = 7S______4L - 7S = 0 ------- eq (i)
   L +  S =   22 ------ eq (ii)
- 4L - 4S = - 88 ------ Multiplying eq (ii) by - 4 to ELIMINATE L ------- eq (iii)
- 11S = - 88 ------ Adding eqs (iii) & (i)
Continue to solve for S, or smaller number. Then substitute the value for S into any of the
2 original equation to determine the value of L, the larger number.