Solve the following systems of linear equations, showing all work: -5y+9x=27       8y-x=-70

Expert Answers
sheryll-pickett eNotes educator| Certified Educator

-5y + 9x=27

8y - x=-70

First find opposites.

You can do this by multiplying the second equation by 9 getting

72y - 9x = -630

Now add this to the first equation. (Add the y terms together, the x terms together and the constants together.  You should find the x terms cancel each other out.)

-5y + 9x=27

72y - 9x = -630

67y = -603

y = -9

Now that you know the value of y, plug the value into both equations...hopefully getting the same answer.

-5(-9) + 9x = 27    8(-9) -x = -70

45 + 9x = 27             -72 - x = -70

9x = -18                     - x = 2

x = -2                           x = -2

Your point of intersection is (-2, -9).  This is also your solution to the system.

krishna-agrawala | Student

The given simultaneous equations are:

- 5y + 9x = 27   ...   (1)

8y - x = -70       ...   (2)

We solve these equations for values of x an y as follows:

Multiplying equation (2) by 9 we get:

72y - 9x = - 630       ...   (3)

Adding equation (1) and (3) we get:

- 5y + 72y + 9x - 9x = 27 - 630

67y = -603

Therefor:

y = - 603/67 = -9

Substituting this value of y in equation (2) we get:

8*(-9)y - x = -70

-72 - x = -70

- x = - 70 + 72 = 2

Therefor x = -2

Answer:

x = -2, and y = -9

neela | Student

-5y+9x=27..........(1)

8y-x=-70.............(2)

To solve  the equations, we use 2nd equation. 8y-x= -70. So -x =-70-8y .Or x=70+8y . We substitute 70+8y for x in eq (1):

-5y+9(-70-8y) =27.

-5y+630+72y = 27.Or

67y = 27-630 = -603. Or

y =-603/67=-9

y=-603/67=-9. Again substituting -9 for x in any of the two given equations,(we substitute in) 2nd eq: 8y-x=-70. Or 8*(-9) =-70. Therefore, -72-x=-70. Or -x= -70+72 =2. So x=2.

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