Question

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

Answer 1

`(1,-5)`

Explanation:

`3color(red)(x)-2y=13to(1)`

`color(red)(x)=-y-4to(2)`

`"Since " (2)" is expressed with x as the subject, we can"`
`"substitute it directly into "(1)" and solve for y"`

`rArr3(-y-4)-2y=13`

`rArr-3y-12-2y=13larr" distributing"`

`rArr-5y-12=13larr" simplifying left side"`

`"add 12 to both sides"`

`-5ycancel(-12)cancel(+12)=13+12`

`rArr-5y=25`

`"divide both sides by - 5"`

`(cancel(-5) y)/cancel(-5)=25/(-5)`

`rArry=-5`

`"substitute this value into "(2)" and evaluate for x"`

`y=-5tox=-(-5)-4=5-4=1`

`color(blue)"As a check"`

Substitute these values for x and y into the left side of ( 1 ) and if equal to the right side then they are the solution.

`"left side "=(3xx1)-(2xx-5)=3+10=13`

`rArr"point of intersection "=(1,-5)`
graph{(y+x+4)(y-3/2x+13/2)=0 [-10, 10, -5, 5]}