Determine if the point is a solution to the system of linear equations \huge \{{ \large \begin{array}{} 2x + 3y = 2 \\ 6y = 5 - 4x \end{array}} ​

Question

Determine if the point is a solution to the system of linear equations
`\huge \{{ \large \begin{array}{} 2x + 3y = 2 \\ 6y = 5 - 4x \end{array}}` ​

Answer 1

The system has no solutions.

Explanation:

If you stare at it for the bit you can tell the system is impossible. Let's see why:

First of all, rewrite the second equation by bringing all unknowns on the LHS:

`4x+6y=5`.

Then take twice the first equation, doubling every coefficient:

`4x+6y=4` See how the LHS is the same? The system is asking you to find a quantity (4x+6y) which is at the same time equal to four AND five - emphasis on that "and" - which is obviously impossible, because it implies that 4=5. So the point - which you didn't provide - is not a solution. Nor is any other point.