Question

How do you solve the following linear system: `2x+3y=13 , 3x+y=3`?

Answer 1

`x,y=-4/7, 4 5/7`

Explanation:

Solve by elimination:

`2x+3y=13,3x+y=3`

If you see carefully you could see that you can eliminate `3y` from the first equation by `y` in the second equation if we multiply it with `-3` to get `-3y`

`rarr-3(3x+y=3)`

`rArr-9x-3y=-9`

Now add both the equations

`rarr(2x+3y=13)+(-9x-3y=-9)`

`rarr-7x=4`

Divide both sides by `-7`

`rarr(cancel(-7)x)/cancel(-7)=-4/7`

`rArrx=-4/7`

Now substitute the value to any of the equations

ie.(in this case for the second equation)

`rarr3(4/-7)+y=3`

`rarr-12/7+y=3`

Add `-12/7` both sides

`rarry=3+12/7`

`rArry=33/7=4 5/7`