Question

How do you solve the system of equations `y=-4x-8` and `y=9x+5`?

Answer 1

`(-1,-4)`

Explanation:

Labelling the equations.

`color(red)(y)=-4x-8to(1)`

`color(red)(y)=9x+5to(2)`

Since both equations are expressed with y as the subject then we can equate the right sides of both equations.

`rArr9x+5=-4x-8`

add 4x to both sides.

`9x+4x+5=cancel(-4x)cancel(+4x)-8`

`rArr13x+5=-8`

subtract 5 from both sides.

`13xcancel(+5)cancel(-5)=-8-5`

`rArr13x=-13`

divide both sides by 13

`(cancel(13) x)/cancel(13)=(-13)/13`

`rArrx=-1`

Substitute this value into either equation ( 1 ) or ( 2 ) and solve for y.

Substitute x = - 1 in ( 2 )

`x=-1toy=(9xx-1)+5=-9+5=-4`

`color(blue)"As a check"`

Substitute x = - 1 into the right side of both equations and if equal to - 4 the they are the solution.

`"right side "=(-4xx-1)-8=4-8=-4`

`"right side "=(9xx-1)+5=-9+5=-4`

`rArr(-1,-4)" is the point of intersection"`
graph{(y+4x+8)(y-9x-5)=0 [-5, 2, -10, 5]}