How do you solve the following system: 2x+7y=1, 6x + 7y = -9 ?

2 Answers
G_Ozdilek
Jul 31, 2017

By arranging it, it can be calculated that x=-5/2 and y=6/7

Explanation:

The first equation can be rewritten
-6x - 21y = -3 (after multiplication by -3)
6x + 7y = -9 (the second original equation)

Combine these two equations:
-14y = -12

y=12/14
or
y=6/7

Now put value in the first original equation:

2x = 1 - (7times(6/7))

2x = 1-6

x=-5/2

The answer is x=-5/2 and y=6/7

EZ as pi
Jul 31, 2017

x= -2.5 and y= 6/7

Explanation:

Note that the number of ys in both equations stays the same.
The difference in the the totals therefore represents the difference in the number of xs. Subtract the two equations:

" "6xcolor(blue)(+7y) =-9" ".........A
" "ul(2xcolor(blue)(+7y) =+1)" ".........B

A-B" "4x = -10" "solve for x

" "x = -2.5

Substitute -2.5 for x to find y in B

2(-2.5) +7y =1

" "-5 +7y = 1
" "7y =1+5
" "7y =6
" "y = 6/7

Check in A:
6xx(-2.5)+7(6/7)

=-15+6 =-9
This is correct.

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