Question

Without drawing the graphs, find the points of intersection of the lines:

11x–6y=2 and –8x+5y=3

Answer 1

(
`(18)/(7)\\` ,
`(92)/(21)` ) or x =
`(18)/(7)` y =

( 2.57 , 4.18) or x = 2.57 y = 4.18

Explanation:

Use elimination:

Find the least common multiple between x or y in this case use -6 and 5 (make sure there are opposite signs)

11x - 6y = 2 multiply entire problem by 5

-8x + 5y = 3 multiply entire problem by 6

55x - 30y = 10 combine problems

-48x + 30y = 18

7x + 0y = 18

7x = 18 =
`(18)/(7)` Plug into one equation to find y

11(
`(18)/(7)`) - 6y = 2

`(198)/(7)` - 6y = 2

-6y = -
`(184)/(7)`

y=
`(92)/(21)`

Hope this helps :)