Question

How do you solve `2x+6y=32` and `5x-2y=12` using substitution?

Answer 1

`therefore` `color(red)(x=4 and y=4`

Explanation:

`2x+6y=32`

`=> x + 3y = 16`

Multiplying both sides by 2

`x=16-3y`

Given that,

`5x−2y=12`

Replacing `x=16-3y`

`5(16-3y)-2y=12`

`80-15y-2y=12`

`80-17y=12`

`17y=80-12`

`17y=68`

`y=68/17`

`color(magenta)(y=4`

`therefore x=16-3y`

`x=16-3xx4`

`x=16-12`

`color(magenta)(x=4`

`therefore` `color(red)(x=4 and y=4`

~Hope this helps! :)

Answer 2

`x=4, y=4`

Explanation:

`2x+6y=32`
`5x-2y=12`

In order to use substitution, rearrange one of the equations

`2x+6y=32`
`2x= -6y+32` (Subtracted 6y from both sides)
`x=-3y+16` (Divided both sides by 2)

Now that we rearrange the equation, we plug it into `5x-2y=12`

`5(-3y+16)-2y=12`
`-15y+80-2y=12` (Distributed 5 to the terms in bracket)
`-17y+80=12` (Combined like terms)
`-17y = -68` (Subtract 80 from both sides)
`y=4` (Divided both sides by -17)

Now that we have the y term, we can plug it into either equation to find x

`2x+6(4) = 32`
`2x+24=32` (Multiplied 6*4)
`2x= 8` (Subtracted 24 from both sides)
`x=4` (Divided both sides by 2)

Check your answer y plugging in y=4 and x=4 into either equation.