Question

How do you solve the following linear system `4x - 3y = -5 , 4x +- 4y = -4`?

Answer 1

For equations `4x-3y=-5` and `4x+4y=-4`, solution `(-8/7, 1/7)`
For equations `4x-3y=-5` and `4x-4y=-4`, solution `(-2, -1)`

Explanation:

We will use `color(blue)("method of elimination of variables")`

For equations `4x-3y=-5` and `4x+4y=-4`

`4x+4y=-4`
`4x-3y=-5`

Perform subtraction to obtain

`7y=1`

then `y=1/7`
Using `4x+4y=-4` and `y=1/7`

We have, `4x+4(1/7)=-4`

`x+1/7=-1`

`x=-8/7`

For equations `4x-3y=-5` and `4x+4y=-4`, solution `(-8/7, 1/7)`

Again, we will use `color(blue)("method of elimination of variables")`

For equations `4x-3y=-5` and `4x-4y=-4`

`4x-4y=-4`
`4x-3y=-5`

Perform subtraction to obtain

`y=-1`

then `y=-1`
Using `4x-4y=-4` and `y=-1`

We have, `4x-4(-1)=-4`

`x-(-1)=-1`

`x+1=-1`

`x=-2`

For equations `4x-3y=-5` and `4x-4y=-4`, solution `(-2, -1)`
graph{(4x-3y+5)(4x+4y+4)(4x-4y+4)=0 [-3, 2, -5, 5]}

God bless....I hope the explanation is useful..