Question

How do you solve `1.3x+y=3` and `7x+2y=1` using substitution?

Answer 1

`y= 197/44`
`x=-50/44`

Explanation:

Given:

`1.3x+y=3`......................(1)
`7x+2y=1`.......................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider equation (1)

Subtract 1.3x from both sides giving

`y=3-1.3x" ".....................(1_a)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute `(1_a)` in (2) giving

`7x+2(3-1.3x)=1`

`7x+6-2.6x=1`

`4.4x+6=1`

Subtract 6 from both sides

`4.4x=-5`

Multiply both sides by 10

`44x=-50`

`color(blue)(x=-50/44)`..................(3)
'~~~~~~~~~~~~~~~~~~~~~~~~

Substitute (3) into (2)

`7(-50/44)+2y=1`

`y=1/2+7/2( 50/44)`

`color(blue)(y=4 21/44 = 197/44)`