Solve Using a Matrix with Cramer's Rule x+y=-4 , y=-3-x-3

Problem

{[x+y=−4],[y=−3−x−3])

Solution

1. Rearrange the second equation into standard form A*x+B*y=C by adding x to both sides and combining constants.

x+y=−6

2. Identify the system of linear equations in standard form.

{[1*x+1*y=−4],[1*x+1*y=−6])

3. Calculate the determinant of the coefficient matrix D

D=|[1,1],[1,1]|

D=(1)*(1)−(1)*(1)=0

4. Analyze the result of the determinant. Since D=0 Cramer's Rule cannot be used to find a unique solution.

5. Determine the nature of the system by checking for consistency. The equations x+y=−4 and x+y=−6 represent parallel lines that never intersect.

Final Answer

No solution (Inconsistent system)

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