1. Solve the system of equations using the linear combination method.

{5m+3n=41 3m-6n=9

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2. Solve the system of equations using the linear combination method.

{6g+8h=40 - 6g+2h=-20

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3. Solve the system of equations using the linear combination method.

{9x+5y=35 2x+5y=0

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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.