Question

How do you solve the following system: `3x + 8y = -2, 2x – 4y = 8`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation to `8y`

• Equation 1:

`3x + 8y = -2`

`3x - color(red)(3x) + 8y = -2 - color(red)(3x)`

`0 + 8y = -2 - 3x`

`8y = -2 - 3x`

• Equation 2:

`2x - 4y = 8`

`2x - color(red)(2x) - 4y = 8 - color(red)(2x)`

`0 - 4y = 8 - 2x`

`-4y = 8 - 2x`

`color(red)(-2) xx -4y = color(red)(-2)(8 - 2x)`

`8y = (color(red)(-2) xx 8) - (color(red)(-2) xx 2x)`

`8y = -16 - (-4x)`

`8y = -16 + 4x`

Step 2) Because the left side of both equations are the same we can equate the right side of each equation and solve for `x`:

`-2 - 3x = -16 + 4x`

`-2 + color(blue)(16) - 3x + color(red)(3x) = -16 + color(blue)(16) + 4x + color(red)(3x)`

`14 - 0 = 0 + (4 + color(red)(3))x`

`14 = 7x`

`14/color(red)(7) = (7x)/color(red)(7)`

`2 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))`

`2 = x`

`x = 2`

Step 3) Substitute `2` for `x` in the solution to either equation in Step 1 and solve for `y`:

`-4y = 8 - 2x` becomes:

`-4y = 8 - (2 xx 2)`

`-4y = 8 - 4`

`-4y = 4`

`(-4y)/color(red)(-4) = 4/color(red)(-4)`

`(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = -1`

`y = -1`

The Solution Is:

`x = 2` and `y = -1`

Or

`(2, -1)`