Question

Solve the system of equations using the linear combination method.

Answer 1

1. 5m+3n=41   
3m-6n=9 (multiplying the first equation by 3 and the second by 5), we get;

15m+9n=123
15m-30n= 45 (subtracting the two equations)         
39n = 78           
     n = 2, and
to get m we substitute n with 2
       3m = 9+6(2)                       
             3m = 21                   
                m = 7
Therefore, n=2 and m=7

2. 6g +8h=40
    -6g +2h = -20(Adding the two equations to eliminate g)
             10 h= 20
                 h =2 
to get g we substitute h with two
6g= 40- 8(2)
    = 24
    g= 4
Therefore, g =4 and h =2

3. 9x +5y =35
    2x + 5y =0 (subtracting the two equations to eliminate y)
           7x =35
             x= 5
To get y we substitute x with 5
5y=35-9(5)
  5y = -10
    y = -2
Therefore, x=5 and y=-2