1. Solve the system of equations using the linear combination method.{5m+3n=41 3m−6n=9Enter your answers in the boxes. 2.Solve the system of equations using the linear combination method.{6g+8h=40 −6g+2h=−20Enter your answers in the boxes.3.Solve the system of equations using the linear combination method.{9x+5y=35 2x+5y=0Enter your answers in the boxes.
Accepted Solution
A:
The linear combination method involves multiplying, adding and subtracting in such a way that allows one variable to be eliminated in the addition or subtraction step. This leaves the other variable alone, allowing its value to be determined.
1. 5m+3n=41, 3m−6n=9 Multiply 1st equation by 2: 10m + 6n = 82 Add to 2nd equation: 13m = 91 Divide by 13: m = 7 Substitute back to 1st equation: n = 2 Therefore m = 7 and n = 2.
2. 6g+8h=40 −6g+2h=−20 Add both equations: 10h = 20 Divide by 10: h = 2 Substitute to 1st equation: g = 4 Therefore g = 4 and h = 2.
3. 9x+5y=35 2x+5y=0 Subtract 1st equation by the 2nd equation: 7x = 35 Divide by 7: x = 5 Substitute back to the 1st equation: y = -2 Therefore x = 5 and y = -2.