solve by elimination method

Question

3r-5s=14

5r+3s=46

 

determine the solution of the system. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a) _ (type an ordered pair)

b) there are infinitely many solutions

c) there are no solutions

Answer 1

The elimination method of solving systems of equations is also called the addition method. To solve a system of equations by elimination we transform the system such that one variable will cancel another variable.

 

We have

3r - 5s = 14
5r + 3s = 46

 

Step 1: multiply equation 1 by 3, and equation 2 by 5 to get

  9r + 15s = 42   and

25r  - 15s = 230

 

Step 2: add both equations to get 34r = 272; r = 8

 

Step 3: substitute the value for r into either equation to get

3(8) - 5s = 14

 

Step 4: expand the equation to get 24 - 5s = 14

 

Step 5: solve for s to get s = 2

 

So, r = 8, and s = 2, and the answer is option A