How do you solve the following system?: 8x +6y =9 , - 5x -7y = -2

2 Answers
May 3, 2017

With some arrangement. x=51/26 and y=-29/26

Explanation:

Expand the first equation with term 5
Expand the second equation with 8.

Now you have:

40x+30y=45
-40x-56y=-16
Now sum these up:
-26y=29

or y=-29/26

Now you can find x using the first or second equation:

8x-(6*29)/26=9

8x=9+(6*29)/26

8x=(117/13) + ((3*29)/13)

8x=204/13

x=204/104

or

x=51/26

x = 1 25/26, y = -1 21/182

Explanation:

8x + 6y = 9 ....................(i)
-5x - 7y = -2 ....................(ii)

You can solve this system by using Elimination method.

You can eliminate either x or y here.
I will eliminate x.

So multiplying eq.(i) by +5 and eq(ii) by +8, you will get

40x + 30y = 45 ......................(iii) &
-40x - 56y = -16 ........................(iv)

Adding eq (iii) and (iv), you will get

-26y = 29

rArr y = -29/26

Substituting y = -29/26 in eq(i), you will get

8x + (-29/26)*6 = 9

rArr 8x = 9 + 87/13

rArr 8x = (117 + 87)/13

rArr 8x = 204/13

rArr x = 204/104 = 51/26