Question

How do you solve the simultaneous equations `4x + 6y = 16` and `x + 2y = 5`?

Answer 1

I found:
`x=1`
`y=2`

Explanation:

You can try multiplying the second equation by `-3` and then add the two equations ogether (in column):
`{4x+6y=16`
`{color(red)(-3x-6y=-15` add:
`x+0=1`
`x=1`
Substitute into the first:
`4*1+6y=16`
`6y=12`
`y=12/6=2`

Answer 2

You can use the substitution method to solve this system of equations.

Explanation:

Your two equations look like this

`{(4x + 6y = 16), (x + 2y = 5) :}`

The first thing you need to do is use of the equations to solve for one of the two variables, `x` or `y`, then use this value into the other equation.

For simplicity, use the second equation to solve for `x` by adding `-2y` to both sides of the equation

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

`x = 5 - 2y`

Now plug this value for `x` in your first equation and solve for `y`

`4 * (5 - 2y) + 6y = 16`

`20 - 8y + 6y = 16`

`20 - 2y = 16`

Isolate `y` on one side of the equation

`-2y + color(red)(cancel(color(black)(20))) - color(red)(cancel(color(black)(20))) = 16 - 20`

`-2y = -4 => y = (-4)/(-2) = 2`

Now take this value and use it to determine `x`

`x = 5 - 2y`

`x = 5 - 2 * 2 = 1`

The two solutions to your system are

`{(x = color(green)(1)), (y=color(green)(2)) :}`