Question

Determine if the point is a solution to the system of linear equations 7B%20%20%5Clarge%20%5Cbegin%7Barray%7D%7B%7D%20%202x%20%2B%203y%20%3D%202%20%20%5C%5C%206y%20%3D%205%20-%204x%20%5Cend%7Barray%7D%7D%20" id="TexFormula1" title=" \huge \{{ \large \begin{array}{} 2x + 3y = 2 \\ 6y = 5 - 4x \end{array}} " alt=" \huge \{{ \large \begin{array}{} 2x + 3y = 2 \\ 6y = 5 - 4x \end{array}} " align="absmiddle" class="latex-formula"> ​

Answer 1

Answer:

The system has no solutions.

Step-by-step 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.