Question

Solve the simultaneous equations
3x - 4y = 8
9x + 5y = -1.5

Answer 1

x =
`(2)/(3)` , y = -
`(3)/(2)`

Explanation:

3x - 4y = 8 → (1)

9x + 5y = - 1.5 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 9x + 12y = - 24 → (3)

add (2) and (3) term by term to eliminate x

0 + 17y = - 25.5

17y = - 25.5 ( divide both sides by 17 )

y =
`(-25.5)/(17)` = -
`(3)/(2)`

substitute this value into either of the 2 equations and solve for x

Substituting into (2)

9x + 5(-
`(3)/(2)` ) = - 1.5

9x -
`(15)/(2)` = -
`(3)/(2)` ( add
`(15)/(2)` to both sides )

9x =
`(12)/(2)` = 6 ( divide both sides by 9 )

x =
`(6)/(9)` =
`(2)/(3)`

Answer 2

y = -1.5

x = 2/3

Explanation:

Step 1. Multiply to eliminate x and solve for y

3(3x - 4y = 8)

9x + 5y = -1.5

Step 2. Eliminate

9x - 12y = 24

- 9x + 5y = -1.5

--------------------------

-17y = 25.5

y = -1.5

Step 3. Re-plug in and solve for x.

9x - 12(-1.5) = 24

9x + 18 = 24

9x = 6

x = 2/3