Question

How do you solve the system of equations `x+ 3y = 27` and `13x - 6y = 36`?

Answer 1

See a solution process below:

Explanation:

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

`x + 3y - color(red)(3y) = 27 - color(red)(3y)`

`x + 0 = 27 - 3y`

`x = 27 - 3y`

Step 2) Substitute `(27 - 3y)` for `x` in the second equation and solve for `y`:

`13x - 6y = 36` becomes:

`13(27 - 3y) - 6y = 36`

`(13 * 27) - (13 * 3y) - 6y = 36`

`351 - 39y - 6y = 36`

`351 + (-39 - 6)y = 36`

`351 + (-45)y = 36`

`351 - 45y = 36`

`-color(red)(351) + 351 - 45y = -color(red)(351) + 36`

`0 - 45y = -315`

`-45y = -315`

`(-45y)/color(red)(-45) = -315/color(red)(-45)`

`(color(red)(cancel(color(black)(-45)))y)/cancel(color(red)(-45)) = 7`

`y = 7`

Step 3) Substitute `7` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 27 - 3y` becomes:

`x = 27 - (3 * 7)`

`x = 27 - 21`

`x = 6`

The solution is: `x = 6` and `y = 7`