Question

How do you solve the system of equations `\frac { 1} { 5} x + \frac { 2} { 3} y = - 1` and `\frac { 2} { 3} x + \frac { 2} { 5} y = 24`?

Answer 1

`color(magenta)(y=-15,x=45`

Explanation:

`:.1/5x+2/3y=-1------(1)`

`:.2/3x+2/5y=24-------(2)`

`(1) xx 150`

`:.150/5x+300/3y=-150`

`:.30x+100y=-150-----(3)`

`(2) xx 45`

`:.90/3x+90/5y=1080`

`:.30x+18y=1080------(4)`

`(3)-(4)`

`:.82y=-1230`

`:.color(magenta)(y=-15`

substitute `color(magenta)(y=-15` in (1)

`:.1/5x+2/3(color(magenta)(-15))=-1`

multiply both sides by`15`

`:.15/5x+30/3(color(magenta)-15)=-15`

`:.3x+10(-15)=-15`

`:.3x-150=-15`

`:.3x=-15+150`

`:.3x=135`

`:.color(magenta)(x=45`

~~~~~~~~~~~~~~~~~~~~~~~~

`color(magenta)(check:`

substitute `color(magenta)(y=-15,x=45` in (2)

`:.2/3(color(magenta)45)+2/5(color(magenta)(-15))=24`

`:.90/3-30/5=24`

`:.30-6=24`

`:.color(magenta)(24=24`