Solve the system of equations using the linear combination method.{5m+3n=413m−6n=9Enter your answers in the boxes.m = n = Solve the system of equations using the linear combination method.{6g+8h=40−6g+2h=−20Enter your answers in the boxes.g = h = Solve the system of equations using the linear combination method.{9x+5y=352x+5y=0Enter your answers in the boxes.x = y =
Accepted Solution
A:
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