Question

How many solutions are there to the following system of equations?. . 2x – y = 2. –x + 5y = 3. A. 1 B. 0 C. 2 D. infinitely many

Answer 1

Hello,

$\Delta=\begin{array}{|cc|}2&-1\\-1&5\end{array}=2*5-(-1)*(-1)=10-1=9\\ \Delta \neq 0 ==\ \textgreater \ 1\ solution$

Answer A

Answer 2

  2 x - y = 2
- x + 5 y = 3   / *2
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  2 x  -  y  =  2
+
- 2 x + 10 y = 6
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           9 y = 8,  y = 8/9
2 x - 8/9 = 2
2 x = 2 + 8 /9
2 x = 26/9
x = 13/9
( x, y ) = ( 13/9,  8/9 )
Answer: A ) 1 solution.