Question

How do you solve the system of equations `4x + 3y = - 9` and `- 5x = 2y + 13`?

Answer 1

`"answer : x=-6 , y=1"`

Explanation:

`4x+3y=-9" , "(1)`
`-5x=2y+13" , "(2)`

`"let us multiply the both sides of equation (1) by 5"`
`color(red)(5*)(4x+3y)=color(red)(5*)(-9)" let us rearrange..."`

`20x+15y=-45" , "(3)`

`"let us multiply the both sides of equation (2) by 4"`
`color(red)(4*)(-5x)=color(red)(4*)(2y+13) " let us rearrange..."`

`-20x=8y+52" , "(4)`

`"let us sum the equation (3) with (4)"`

`cancel(20x)+15ycancel(-20x)=-45+8y+52`

`"we have eliminated the term 'x' "`

`15y=8y+7`

`15y-8y=7`

`7y=7y`

`y=7/7`

`y=1`

`"now, let us write y=1 in one of the any equations above."`

`4x+15*1=-9" , "(1)`
`4x+15=-9`

`4x=-9-15`

`4x=-24`

`x=-24/4`

`x=-6`