Question

How do you solve the following system: `x + 8y = 15 , 5x - 7y = 12`?

Answer 1

See a solution process below:

Explanation:

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

`x + 8y = 15`

`x + 8y - color(red)(8y) = 15 - color(red)(8y)`

`x + 0 = 15 - 8y`

`x = 15 - 8y`

Step 2) Substitute `(15 - 8y)` for `x` in the second equation and solve for `y`:

`5x - 7y = 12` becomes:

`5(15 - 8y) - 7y = 12`

`(5 xx 15) - (5 xx 8y) - 7y = 12`

`75 - 40y - 7y = 12`

`75 + (-40 - 7)y = 12`

`75 + (-47)y = 12`

`75 - 47y = 12`

`75 - color(red)(75) - 47y = 12 - color(red)(75)`

`0 - 47y = -63`

`-47y = -63`

`(-47y)/color(red)(-47) = -63/color(red)(-47)`

`y = 63/47`

Step 3) Substitute `63/47` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 15 - 8y` becomes:

`x = 15 - (8 xx 63/47)`

`x = 15 - 504/47`

`x = (47/47 xx 15) - 504/47`

`x = 705/47 - 504/47`

`x = 201/47`

The Solution Is:

`x = 201/47` and `y = 63/47`

Or

`(201/47, 63/47)`