Question

How do you solve the system `3x+2y=-17` and `2x-5y=14` by substitution?

Answer 1

`x =-3 and y =-4`

Explanation:

Substitution would certainly not be my method of choice for this example, but here goes...

You need to have one of the equations with `x` or `y` as the subject, ie as a single variable,

`2x -5y = 14` can be written as `color(blue)(x= (5y+14)/2)`

Now substitute that expression for `x` in the other equation:

`3color(blue)(x)+2y=-17`

`3color(blue)(((5y+14)/2)) +2y =-17: "larr` now solve for `y`

`3(5y+14)+4y=-34" "larr xx2`

`15y+42+4y=-34`

`19y = -34-42`

`19y = -76`

`y=-4`

Now find `x` by substituting `y=-4`

`color(blue)(x= (5(-4)+14)/2)`

`x =-3`

Check:

`3x+2y`

`=3(-3)+2(-4)`

`-9-8`

`= -17`

Answer 2

`y=-4,x=-3`

Explanation:

`3x+2y=-17------(1)`

`2x-5y=14-------(2)`

`(1)xx2:-`

`:.6x+4y=-34------(3)`

`(2)xx3:-`

`:.6x-15y=42------(4)`

`(3)-(4):-`

`:.19y=-76`

`:.y=-4`

substitute `y=-4` in (1)#

`:.3x+2(-4)=-17`

`:.3x-8=-17`

`:.3x=-17+8`

`:.3x=-9`

`:.x=-9/3`

`:.x=-3`
~~~~~~~~~~~~~~
substitute `y=-4,x=-3` in (2)

`:.2(-3)-5(-4)=14`

`:.-6+20=14`

`:.14=14`