Question

2x+3y=15
x+y=6
work out the values of x and y.

Answer 1

`2x + 3y = 15...(1) \\ x + y = 6...(2) \\ 2 * (2) \\ 2x + 2y = 12...(3) \\ (1) - (3) \\ 0 + 3y - 2y = 15 - 12 \\ \color{red} \boxed{ y = 3 }\\ sub \: in \: (2) \\ x + 3 = 6 \rightarrow \: x = 6 - 3 \\ \color{green} \boxed{ x = 3 }`

Answer 2

Explanation:

Elimination sounds the easiest for y:

`I - 2II: 2x+3y -2x -2y = 15-12 \rightarrow y= 3`

Now we got one value, let's replace in one of the two and find the second

`II: x+(3)=6 \rightarrow x=3`