Question

How do you solve the system of equations `12x + y = 38` and `4x + 5y = 22`?

Answer 1

Se the entire solution process below:

Explanation:

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

`12x + y = 38`

`12x + y - color(12x) = 38 - color(12x)`

`12x - color(12x) + y = 38 - color(12x)`

`0 + y = 38 - 12x`

`y = 38 - 12x`

Step 2) Substitute `38 - 12x` for `y` in the second equation and solve for `x`:

`4x + 5y = 22`

`4x + 5(38 - 12x) = 22`

`4x + 190 - 60x = 22`

`190 - 60x + 4x = 22`

`190 - 56x = 22`

`190 - color(red)(190) - 56x = 22 - color(red)(190)`

`0 - 56x = -168`

`-56x = -168`

`(-56x)/color(red)(-56) = -168/color(red)(-56)`

`(color(red)(cancel(color(black)(-56)))x)/cancel(color(red)(-56)) = 3`

`x = 3`

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

`y = 38 - 12x`

`y = 38 - (12 xx 3)`

`y = 38 - 36`

`y = 2`

The solution is `x = 3` and `y = 2`