Question

Solve the system of equations using the linear combination method.

{5m+3n=41
3m−6n=9

Enter your answers in the boxes.

m =

n =


Solve the system of equations using the linear combination method.

{6g+8h=40
−6g+2h=−20

Enter your answers in the boxes.

g =

h =


Solve the system of equations using the linear combination method.

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

Enter your answers in the boxes.

x =

y =

Answer 1

1. n=2 and m=7

2. g =4 and h =2

3. x=5 and y=-2

Explanation:

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Answer 2

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