Question

How do you solve the following system: `3x + 8y = -2, -2x + 5y = 20`?

Answer 1

See a solution process below:

Explanation:

Step 1: Solve each equation for `6x`:

• Equation 1: `3x + 8y = -2`

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

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

`3x = -2 - 8y`

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

`6x = (color(red)(2) * -2) - (color(red)(2) * 8y)`

`6x = -4 - 16y`

• Equation 2: `-2x + 5y = 20`

`-2x + 5y - color(red)(5y) = 20 - color(red)(5y)`

`-2x + 0 = 20 - 5y`

`-2x = 20 - 5y`

`color(red)(-3) * -2x = color(red)(-3)(20 - 5y)`

`6x = (color(red)(-3) * 20) - (color(red)(-3) * 5y)`

`6x = -60 - (-15y)`

`6x = -60 + 15y`

Step 2: Now with the left side of both equations equal we can equate the right side of the equations and solve for `y`:

`-4 - 16y = -60 + 15y`

`color(blue)(60) - 4 - 16y + color(red)(16y) = color(blue)(60) - 60 + 15y + color(red)(16y)`

`56 - 0 = 0 + (15 + color(red)(16))y`

`56 = 31y`

`56/color(red)(31) = (31y)/color(red)(31)`

`56/31 = (color(red)(cancel(color(black)(31)))y)/cancel(color(red)(31))`

`56/31 = y`

`y = 56/31`

Step 3: Substitute `56/31` for `y` in the solution to either equation in Step 1 and solve for `x`:

`6x = -60 + 15y` becomes:

`6x = -60 + (15 * 56/31)`

`6x = (31/31 * -60) + 840/31`

`6x = -1860/31 + 840/31`

`6x = -1020/31`

`color(red)(1/6) * 6x = color(red)(1/6) * -1020/31`

`6/6x = -170/31`

`x = -170/31`

The Solution Is: `x = -170/31` and `y = 56/31` or `(-170/31, 56/31)`