Question

How do you solve the system of equations `20x - 16y = 28` and `10x - 8y = 14`?

Answer 1

The two equations are different forms of the same equation and therefore cannot be solved to give a final solution. There are infinitely many solutions.

Explanation:

If there are 2 variables in an equation, there in an infinite number of solutions. If a definite solution is to be found, two different equations are needed, which can then be solved as a system - other wise known as simultaneous equations.

in this case we have the equations :

`20x-16y = 28" and "10x-8y =14`

However it should be noted that the first equation is simply twice the second one.
In fact they can both be simplified to give the same equation.

`20x-16y = 28" "rarr div 4" " rarr 5x-4y=7`

`10x-8y =14" "rarr div 2" "rarr 5x-4y =7`

Therefore there are not two different equations and the given equations cannot be solved as a system, or as simultaneous equations.

There is an infinite number of solutions.

For any `x` value that is chosen, a corresponding `y` value can be found.

`x = 1 and y = -1/2`
`x=0 and y=-1 3/4`
`x= 1 2/5 and y= 0`
etc...