Question

Solve this system of equations using the addition method.
.5m + .7n = 6.4
.2m - .7n = .6 @mathstudent55

Answer 1

Add the two equations together, like you're adding some multi-digit numbers on paper:

\[.5m + .7n = 6.4\]\[.2m-.7n = .6\]----------------
\[.7m + 0n = 7.0\]
Can you solve for \(m\) now?

Answer 2

no

Answer 3

why not?

Answer 4

\[.7m = 7.0\]

Answer 5

Divide both sides by the number in front of the letter you are solving for.
\[\frac{.7m}{.7} = \frac{7.0}{.7}\]\[m=\]

Answer 6

m=10 right

Answer 7

exactly! that wasn't so hard, was it?

Answer 8

now we have to find the value of \(n\). we can plug \(m = 10\) into either one of the equations and find \(n\)

Answer 9

but tht wasnt the right answer

Answer 10

but still i dont get ut

Answer 11

what do you mean it wasn't the right answer? what do you think the right answer is?

Answer 12

idk

Answer 13

why are you saying it isn't the right answer?

Answer 14

i check it and and its not

Answer 15

You checked it wrong :-)

Let's continue on to find \(n\) if \(m=10\)
\[.5m + .7n = 6.4\] (first equation)
\[.5(10) + .7n = 6.4\]\[5+.7n=6.4\]Subtract 5 from both sides\[.7n=1.4\]divide both sides by .7\[n = 2\]
Now we check our work:
\[.5(10)+.7(2) = 5 + 1.4 = 6.4\checkmark\]Must also check any other equations!\[.2(10)-.7(2) = 2-1.4=0.6\checkmark\]

Answer 16

so whats the answer

Answer 17

We need to check the solutions in all of the equations in the system because it is possible to find a set of numbers which will satisfy some of the equations but not all of them. For example, m=12.8, n = 0 satisfies the first equation: .5(12.8)+.7(0) = 6.4 but it does not satisfy the second one: .2(12.8)-.7(0) = 2.56

Answer 18

Read my posts again, you'll see the answer.

Answer 19

2.56

Answer 20

no...

Come on, read through them from the beginning of the thread. I came up with a value for m which you insisted was wrong. Then I found the value for n, and I checked them both. Look at the equations which have checkmarks and you'll see the numbers.

Answer 21

This is a system of equations with two variables (m, n), so we will have 2 numbers as "the answer" (m=, n=).