Question

How do solve the following linear system?: `2x+6y=5 , x-7y=4`?

Answer 1

`x=2 19/20; y=-3/20`

Explanation:

`2x+6y=5 (1)`
`x - 7y=4 (2)` Multiplying Equation (2) by 2 and then subtracting from equation (1) We get
`2x+6y=5 (1)`
`2x-14y=8 (2)`

---

`20*y=-3` `:. y=-3/20 and x= 4+ 7*(-3/20) =4-21/20=59/20`{Ans]

Answer 2

`x,y=2 19/20,-3/20`

Explanation:

Solve by elimination:

`color(blue)(2x+6y=5),color(green)(x-7y=4)`

We can eliminate `2x` from the first equation by `x` in the second equation by multiplying it with `-2` to get `-2x`.

`rarr-2(x-7y=4)`

`rarr-2x+14y=-8`

Add both the equations:

`rarr(2x+6y=5)+(-2x+14y=-8)`

`rarr20y=-3`

`rarry=-3/20`

Substitute the value to the first equation:

`rarr2x+6(-3/20)=5`

`rarr2x+(-18/20)=5`

`rarr2x+(-9/10)=5`

`rarr2x-9/10=5`

`rarr2x=5+9/10`

`rarr2x=59/10`

`rarrx=59/10-:2`

`rarrx=59/10*1/2`

`rarrx=59/20=2 19/20`