it uses linear equations

Question

To use the linear combination method and addition to eliminate the x-terms, by which number should the first equation be multiplied?

5x+10y=15

10x+3y= 13

Answer 1

2[5x +10y =15]  The first equation must be multiplied by 2.

   10x+3y = 13

 

  10x+20y =30

-(10x+ 3y = 13)

          17y = 17

             y = 1

 

10x +3(1) = 13

  10x = 10

     x = 1

 

The solution is (1, 1).

Answer 2

Multiply the first equation by -2 and then add both equations.  That will eliminate the x terms.