Question

How do you solve `5x - 1/2y = 24` and `3x - 2/3y = 41/3`?

Answer 1

`{(x = 5), (y = 2) :}`

Explanation:

You can solve this system of equations by multiplication.

Start by rewriting your two equations so that you can work without denominators.

`{(10x - y = 48), (9x - 2y = 41):}`

Notice that you can multiply the first equation by `-2` so that you get

`10x - y = 48 | * (-2)`

`-20x + 2y = - 96`

You can now add the two equations to cancel the `y`-terms and solve for `x`. Add the left side of the equations and the right side of the equations separately to get

`-20x + color(red)(cancel(color(black)(2y))) + 9x - color(red)(cancel(color(black)(2y))) = -96 + 41`

`-11x = -55 implies x= ((-55))/((-11)) = color(green)(5)`

Use the value of `x` in either one of the two equations to find the value of `y`

`10 * 5 - y = 48`

`y = 50 - 48 = color(green)(2)`

The two solutions to this system of equations are

`{(x = 5), (y = 2) :}`