SOLUTION: 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 equa

Algebra.Com
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!
Found 2 solutions by ptaylor, MathTherapy:
Answer by ptaylor(2198)   (Show Source): You can put this solution on YOUR website!
Here's a good way to start:
Let x= larger number
And let y= smaller. umber
Now we are told that:
4x=7y--------eq1
We are also told that:
x+y=22-----eq2
Substitution method looks easier.
From eq1 x=(7/4)y. Substitute this into eq2
(7 /4)y +y=22
(7/4)y+(4/4)y=22
(11/4)y=22 multiply each side by 4
11y=88
y=8
From eq2, x+8=22
x=14
Hope this helps ---ptaylor
Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!

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!
Method 1: SUBSTITUTION

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.



Method 2: ELIMINATION

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. 

RELATED QUESTIONS


the question is solving the equation using the substitution method or the elimination... (answered by mananth)

how do i y=2x and x+y=12 by solving system of equations by the substitution... (answered by stanbon)

Hi! How do I do the substitution method? I am so confused. So, what is the solution on... (answered by rfer)

Systems of equations can be solved by graphing or by using substitution or elimination.... (answered by stanbon)

Please help with solving the systems of equations by substitution and elimination.  Once... (answered by longjonsilver)

Describe 2 advantages of the substitution method over the graphing method for solving... (answered by stanbon)

I need help solving a few questions on Chapter 4.3 Solving Systems of Linear Equations by  (answered by Alan3354)

Hello, we are learning the substitution method of solving systems of equations.  My... (answered by drk)

When solving Linear Systems algebraically, there are the three main methods;... (answered by alaccalac)