Question

How do solve the following linear system?: `5x+2y=4 , 3x – 4y = 7`?

Answer 1

Solve by substitution and elimination:

`5x+2y=4`

`3x-4y=7`

We can eliminate `-4y` from the second equation by `2y` in the first equation if we multiply it with `2` to get `4y`

`rarr2(5x+2y=4)`

`rarr=10x+4y=8`

Add both of the equations:

`rarr(10x+4y=8)+(3x-4y=7)`

`rarr=13x=15`

`rarrx=15/13`

Now substitute the value of `x` to the first equation:

`rarr5(15/13)+2y=4`

`rarr75/13+2y=4`

`rarr75/13+(26y)/13=4`

`rarr(75+26y)/13=4`

`rarr75+26y=13*4`

`rarr75+26y=52`

`rarr26y=52-75`

`rarr26y=-23`

`rarry=-23/26`

So,`(x,y)=(15/13,-23/26)`