Question

How do you solve the following system?: `x +7y = 3 , 12x -9 y = 2`

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`x + 7y = 3`

`x + 7y - color(red)(7y) = 3 - color(red)(7y)`

`x + 0 = 3 - 7y`

`x = 3 - 7y`

Step 2) Substitute `(3 - 7y)` for `x` in the second equation and solve for `y`:

`12x - 9y = 2` becomes:

`12(3 - 7y) - 9y = 2`

`(12 xx 3) - (12 xx 7y) - 9y = 2`

`36 - 84y - 9y = 2`

`36 + (-84 - 9)y = 2`

`36 + (-93)y = 2`

`36 - 93y = 2`

`36 - color(red)(36) - 93y = 2 - color(red)(36)`

`0 - 93y = -34`

`-93y = -34`

`(-93y)/color(red)(-93) = -34/color(red)(-93)`

`(color(red)(cancel(color(black)(-93)))y)/cancel(color(red)(-93)) = 34/93`

`y = 34/93`

Step 3) Substitute `34/93` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 3 - 7y` becomes:

`x = 3 - (7 xx 34/93)`

`x = (93/93 xx 3) - 238/93`

`x = 279/93 - 238/93`

`x = 41/93`

The Solution Is:

`x = 41/93` and `y = 34/93`

Or

`(41/93, 34/93)`