Question

Determine the number solutions for system x-2y=1 and -4x+8y=-4

Answer 1

Hence, the system of equation does not have solution.

Explanation:

You have the following 2x2 system:

`x-2y=1\ \ \ \ (1)\\\\-4x+8y=-4\ \ \ \ (2)`

You can obtain the solution to the system by using substitution method.

You solve the first equation for x:

`x=1+2y` (3)

Next, you replace (3) in the equation (2), and you solve for y:

`-4(1+2y)+8y=-4\\\\-4-8y+8y=-4\\\\0=0`

The last result is the trivial solution. This means that the equation (2) is a multiple scale of the first equation. In fact, if you multiply equation (1) by -4, you obtain the equation (2).

Hence, the system of equations does not have solution.