Question

Solve the system of equations using the substitution method.

{2x+8y=4
x=−3y+5

x=
y=


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

x = -4 and y = -3 this is the answer

Answer 2

Solution:

1) Given system of equations

2x+8y = 4 ----(1)

x = -3y+5 ----(2)

Substitute (2) in equation (1), we get

=> 2(-3y+5)+8y=4

=> -6y+10+8y = 4

=> 2y+10 = 4

=> 2y = 4-10

=> 2y = -6

=> y = (-6)/2

=> y = -3

Now , substitute y = -3 in

equation (2) , we get

=> x = -3(-3)+5

=> x = 9 + 5

=> x = 14

Therefore,

x = 14 , y = -3

2) 5m+3n = 41 ---(3)

3m-6n = 9 ---(4)

multiply equation (3) by 2 , we

get

=> 10m+6n=82 ----(5)

Add equations (4) and (5) , we get

=> 13m = 91

=> m = 91/13

=> m = 7

substitute m=7 in equation (4),

we get

=> 3×7 - 6n = 9

=> 21 - 6n = 9

=> -6n = 9-21

=> -6n = -12

=> n = (-12)/(-6)

=> n = 2

Therefore,

m = 7 , n = 2

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