Question

How do you solve the system of equations `4x + 3y = - 19` and `7x + 27= y`?

Answer 1

`x= -4, y = -1`

Explanation:

`4x + 3y = -19` (1)
`7x - y = -27` (2)

Multiply Eqn (2) by 3 and then add.

`4x +3y = -19`
`21x - 3y = -81`

Adding both to eliminate y,
`25x = -100`
`x = -4`

Substituting value of x in (1),
`-16 + 3y = -19`
`3y = -3`
`y = -1`

Answer 2

`(x,y)to(-4,-1)`

Explanation:

`4x+3y=-19to(1)`

`7x+27=color(red)(y)to(2)`

`"equation "(2)" gives y in terms of x and so can be "`
`color(blue)"substituted ""into "(1)"`

`rArr4x+3(7x+27)=-19`

`rArr4x+21x+81=-19`

`"subtract 81 from both sides "`

`25xcancel(+81)cancel(-81)=-19-81`

`rArr25x=-100`

`"divide both sides by 25"`

`rArrx=-4`

`"substitute this value in "(2)" and solve for y"`

`rArry=(7xx-4)+27=-28+27=-1`

`rArr"point of intersection "=(-4,-1)`
graph{(y-7x-27)(y+4/3x+19/3)=0 [-10, 10, -5, 5]}