Question

How do you solve this system of equations: `y-x = -5, x+y = 8`?

Answer 1

See a solution process below:

Explanation:

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

`y - x = -5`

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

`y - 0 = -5 + x`

`y = -5 + x`

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

`x + y = 8` becomes:

`x + (-5 + x) = 8`

`x - 5 + x = 8`

`1x + 1x - 5 = 8`

`2x - 5 = 8`

`2x - 5 + color(red)(5) = 8 + color(red)(5)`

`2x - 0 = 13`

`2x = 13`

`(2x)/color(red)(2) = 13/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 13/2`

`x = 13/2`

Step 3) Substitute `13/2` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -5 + x` becomes:

`y = -5 + 13/2`

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

`y = -10/2 + 13/2`

`y = 3/2`

**The Solution Is: `x = 13/2` and `y = 3/2` or `(13/2, 3/2)`

Answer 2

The point of intersection is `(13/2,3/2)`.

Refer to the explanation for the process.

Explanation:

Solve the system:

These are linear equations. Since they are a system, both equations are solved simultaneously. The resulting values for `x` and `y` is the point at which the two lines intersect on a graph.

`y-x=-5,` `x+y=8`

Solve the first equation for `y`.

`y=x-5`

Substitute `x-5` for `y` into the second equation and solve.

`x+(x-5)=8`

Simplify parentheses.

`x+x-5=8`

Simplify.

`2x-5=8`

Add `5` to both sides.

`2x=8+5`

Simplify.

`2x=13`

Divide both sides by `2`.

`x=13/2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute `13/2` for `x` in the first equation.

`y-13/2=-5`

Add `13/2` to both sides.

`y=13/2-5`

Multiply `-5` by `2/2` to make the denominators the same.

`y=13/2-5/1xx2/2`

Simplify.

`y=13/2-10/2=3/2`

`y=3/2`

The point of intersection is `(13/2,3/2)`.