What is the point of intersection of (x-2y=4) and (2x-y=5)?

Correct answer: ( (2,-1) )

The direct answer is A: \((2,-1)\). A point of intersection must satisfy both equations. Test A: with \(x=2,y=-1\), the first left side is \(x-2y=2-2(-1)=2+2=4\), and the second is \(2x-y=2(2)-(-1)=4+1=5\). Both equations hold, so A is correct. B, \((-2,1)\), gives \(-2-2(1)=-4\), not 4. C, \((1,-2)\), gives \(1-2(-2)=5\), not 4, although its second value is 4-? actually \(2(1)-(-2)=4\), not 5. D, \((3,-1)\), gives \(3-2(-1)=5\), not 4, and \(6+1=7\), not 5. Thus only A satisfies both. The negative y-coordinate is important: subtracting a negative number becomes addition. Memory cue: substitute both coordinates into both equations and check both results.