Question

What is the solution for the system of equations {9x+8y=3 6x−12y=−11?

Answer 1

( -
`(1)/(3)`,
`(3)/(4)` )

Explanation:

Given the 2 equations

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

To eliminate the y- term multiply (1) by 1.5

13.5x + 12y = 4.5 → (3)

Add (2) and (3) term by term

(6x + 13.5x) + (- 12y + 12y) = (- 11 + 4.5)

19.5x = - 6.5 ( divide both sides by 19.5 )

x =
`(-6.5)/(19.5)` = -
`(1)/(3)`

Substitute this value into either of the 2 equations and solve for y

Using (1), then

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y =
`(6)/(8)` =
`(3)/(4)`

Solution is (-
`(1)/(3)`,
`(3)/(4)` )