Question

How do you solve the following system: `3x+5y=5 , 4x+y=10`?

Answer 1

See the entire solution process below:

Explanation:

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

`4x + y - color(red)(4x) = 10 - color(red)(4x)`

`4x - color(red)(4x) + y = 10 - color(red)(4x)`

`0 + y = 10 - 4x`

`y = 10 - 4x`

Step 2) Substitute `color(red)(10 - 4x)` for `y` in the first equation and solve for `x`:

`3x + 5(10 - 4x) = 5`

`3x + 50 - 20x = 5`

`3x - 20x + 50 = 5`

`-17x + 50 = 5`

`-17x + 50 + color(red)(17x) - color(blue)(5) = 5 + color(red)(17x) - color(blue)(5)`

`-17x + color(red)(17x) + 50 - color(blue)(5) = 5 - color(blue)(5) + color(red)(17x)`

`0 + 50 - 5 = 0 + 17x`

`45 = 17x`

`45/color(red)(17) = (17x)/color(red)(17)`

`45/17 = (color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17))`

`45/17 = x`

`x = 45/17`

Step 3) Substitute `color(red)(45/17)` for `x` in the solution to the second equation at the end of Step 1:

`y = 10 - (4 xx 45/17)`

`y = (17/17 xx 10) - (180/17)`

`y = 170/17 - 180/17`

`y = -10/17`

The solution is: `x = 45/17`, `y = -10/17` or `(45/17, -10/17)`