Question

How do you solve the following system: #2x+y=5, -29=5y-3x #?

Answer 1

See a solution process below:

Explanation:

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

`2x + y = 5`

`-color(red)(2x) + 2x + y = -color(red)(2x) + 5`

`0 + y = -2x + 5`

`y = -2x + 5`

Step 2) Substitute `(-2x + 5)` for `y` in the second equation and solve for `x`:

`-29 = 5y - 3x` becomes:

`-29 = 5(-2x + 5) - 3x`

`-29 = (5 xx -2x) + (5 xx 5) - 3x`

`-29 = -10x + 25 - 3x`

`-29 = -10x - 3x + 25`

`-29 = (-10 - 3)x + 25`

`-29 = -13x + 25`

`-29 - color(red)(25) = -13x + 25 - color(red)(25)`

`-54 = -13x + 0`

`-54 = -13x`

`(-54)/color(red)(-13) = (-13x)/color(red)(-13)`

`54/13 = (color(red)(cancel(color(black)(-13)))x)/cancel(color(red)(-13))`

`54/13 = x`

`x = 54/13`

Step 3) Substitute `54/13` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -2x + 5` becomes:

`y = (-2 xx 54/13) + 5`

`y = -108/13 + 5`

`y = -108/13 + (13/13 xx 5)`

`y = -108/13 + 65/13`

`y = -43/13`

The Solution Is: `x = 54/13` and `y = -43/13` or `(54/13, -43/13)`