SOLUTION: Solve by the substitution method 7m+n=27 m-8n=69

Question 200627: Solve by the substitution method
7m+n=27
m-8n=69
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by 8.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and .

This means that the system is consistent and independent.

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
(1) 7m +n = 27
(2) m-8n = 69 ,,,,,,,m= (8n +69)
.
subst (2) in (1)
.
7(8n+69) +n = 27
56n +483 +n = 27
57n = -456
n = -8
.
subst in (2) m= (8n +69) = 8(-8) -69 = -64 +69 = 5
.
Answer ,,,,,m=5,,,,n=-8
.
check
(1) 7(5) +(-8) = 35 -8 = 27,,,,,ok
(2) (5) -8(-8) = 5+64 =69,,,,,,,,ok
.
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