Question

4x – 2y = 20-8x + 4y = -40

Answer 1

We have the system of equations:

`\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}`

We can tell that the equations are linear combination of each other: if we multiply the first equation by -2 we get the second equation.

`\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}`

So in fact we have only one equation and two unknowns, so there are infinite solutions to this system.

We can write the solution as:

`\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}`

Answer: the system has infinte solutions, expressed in the line y=-2x+10.