Question

Solve the system using elimination. –10x – 3y = –18 –7x – 8y = 11

Answer 1

x = 3 and y = -4

Explanation:

It is given that,

-10x – 3y = –18 ----(1)

–7x – 8y = 11 -------(2)

Solve equation using elimination

-10x – 3y = –18 ----(1)

10x + 3y = 18

Multiply by 7

70x + 21y = 126 ----(3)

–7x – 8y = 11 -------(2)

-70x - 80y = 110 ---(4)

(3) +(4)

21y - 80y = 126 + 110

-59y = 236

y = 236/(-59) = -4

-10x – 3y = –18 ----(1)

-10x - (3 * -4) = -18

-10x + 12 = -18

-10x = -30

x = 30/10 = 3

Therefore x = 3 and y = -4

Answer 2

x=3, y=-4

EXPLANATION

The given system is :

First equation:

`- 10x - 3y = - 18`

Second equation:

`- 7x - 8y = 11`

Let us multiply the first equation by 7 to get,

Third equation;

`- 70x - 21y = - 126`

Let us multiply the second equation too by 10 to get,

Fourth equation:

`- 70x - 80y = 110`

Subtract the fourth equation from the third equation:

`- 21y + 80y = - 126 - 110`

`59y = -236`

Divide both sides by 59.

`y = - 4`

Put y=-4 into the second equation and solve for x.

`- 7x - 8( - 4) = 11`

`- 7x + 32 = 11`

`- 7x = 11 - 32`

`- 7x = - 21`

`x = 3`

The solution is x=3, y=-4