Answer:
Part 1) No solutions
Part 2) \(y=9\)
part 3) \((0,-3)\)
Step-by-step explanation:
Part 1) we have
\(3x-2y=6\) -------> equation A
\(6x-4y=14\) -------> equation B
Multiply the equation A by \(2\)
\(2(3x-2y)=2*6\) --------> \(6x-4y=12\)
Equation A and equation B represent parallel lines
therefore
Is a inconsistent system of equations
The system has no solution
Part 2) we have
\(5x+4y=1\) -------> equation A
\(4x+3y=-1\) -------> equation B
Multiply equation A by \(4\)
\(4*(5x+4y)=4*1\) ------> \(20x+16y=4\) ------> equation C
Multiply equation B by \(-5\)
\(-5*(4x+3y)=-5*-1\) ------> \(-20x-15y=5\) ------> equation D
Adds equation C and equation D
\(20x+16y=4\\-20x-15y=5\\---------\\16y-15y=4+5\\y=9\)
Part 3) we have
\(y< 2x+4\) -------> inequality A
\(y< -2x+2\) -------> inequality B
we know that
If a ordered pair lie in the solution set of the system of inequalities
then
the ordered pair must be satisfy the system of inequalities
case A) \((1,0)\)
substitute the value of x and the value of y in both inequalities
Verify inequality A
\(0< 2(1)+4\)
\(0< 6\) -------> is true
Verify inequality B
\(0< -2(1)+2\)
\(0< 0\) ------> is not true
the point \((1,0)\) is not a solution
case B) \((-5,-2)\)
substitute the value of x and the value of y in both inequalities
Verify inequality A
\(-2< 2(-5)+4\)
\(-2< -6\) -------> is not true
the point \((-5,-2)\) is not a solution
case C) \((0,-3)\)
substitute the value of x and the value of y in both inequalities
Verify inequality A
\(-3< 2(0)+4\)
\(-3< 4\) -------> is true
Verify inequality B
\(-3< -2(0)+2\)
\(-3< 2\) ------> is true
the point \((0,-3)\) is a solution
case D) \((-1,5)\)
substitute the value of x and the value of y in both inequalities
Verify inequality A
\(5< 2(-1)+4\)
\(5< 2\) -------> is not true
the point \((-1,5)\) is not a solution
