One number is seven more than a second number. Six times the first is 10 less than 2 times the second. Find the numbers.

The value of the first number is ___.
The value of the second number is ___.

Step-by-step explanation:

The first number is

−

13

and the second number is

−

6

Explanation:

Let's let the first number be

n

and the second number be called

m

.

Then, from the first sentence we can write:

n

=

m

−

7

and from the second sentence we can write:

2

n

=

6

m

+

10

Substitute

m

−

7

for

n

in the second equation and solve for

m

:

2

(

m

−

7

)

=

6

m

+

10

2

m

−

14

=

6

m

+

10

2

m

−

14

−

2

m

−

10

=

6

m

+

10

−

2

m

−

10

−

14

−

10

=

6

m

−

2

m

−

24

=

4

m

−

24

4

=

4

m

4

m

=

−

6

Now substitute

−

6

for

m

in the first equation and calculate

n

:

n

=

−

6

−

7

n

=

−

13

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