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Sagot :
We have the system of equations:
[tex]\begin{gathered} 4x-2y=20 \\ -8x+4y=-40 \end{gathered}[/tex]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.
[tex]\begin{gathered} -2(4x-2y)=-2(20) \\ -8x+4y=-40 \end{gathered}[/tex]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:
[tex]\begin{gathered} 4x-2y=20 \\ 2y=20-4x \\ y=10-2x \\ y=-2x+10 \end{gathered}[/tex]Answer: the system has infinte solutions, expressed in the line y=-2x+10.
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