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3 votes
Solve this system by the substitution method:
n = 4m
M-n=9

User Ivan Yurov
by
8.9k points

1 Answer

5 votes

Answer:

Step-by-step explanation:

m

=

1

;

n

=

2

Step-by-step explanation:

Given:

4

m

+

n

=

2

-------------------------------Equation (1)

m

4

n

=

9

..........................................Equation (2)

Determine the value of n

Showing every step in the first part to demonstrate method

Consider Equation (2)

Add 4n to both sides

m

4

n

+

4

n

=

9

+

4

n

But

4

n

4

n

=

0

m

=

9

+

4

n

.....................................(3)

Substitute for m in (1) using (3)

4

m

+

n

=

2

4

(

9

+

4

n

)

+

n

=

2

Multiply out the bracket

36

+

16

n

+

n

=

2

36

+

17

n

=

2

Subtract 36 from both sides

17

n

=

34

Divide both sides by 17

n

=

34

17

=

2

'.........................................................

Determine the value of m

Substitute

n

=

2

into (2)

m

4

n

=

9

m

4

(

2

)

=

9

m

+

8

=

9

m

=

9

8

m

=

1

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Check

4

m

+

n

=

2

4

(

1

)

+

(

2

)

=

2

m

4

n

=

9

1

4

(

2

)

=

9

User Josef Grahn
by
8.0k points

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