Find the Variables [[1,2],[-3,-6]]*[[x],[y]]=[[4],[-2]]

Problem

[[1,2],[−3,−6]]*[[x],[y]]=[[4],[−2]]

Solution

1. Perform matrix multiplication on the left side of the equation by multiplying each row of the first matrix by the column vector.

1*(x)+2*(y)=4

−3*(x)−6*(y)=−2

2. Simplify the system of linear equations to see the relationship between the two equations.

x+2*y=4

−3*x−6*y=−2

3. Multiply the first equation by −3 to compare it directly with the second equation.

−3*(x+2*y)=−3*(4)

−3*x−6*y=−12

4. Compare the equations to check for consistency.

−3*x−6*y=−12

−3*x−6*y=−2

5. Identify the contradiction since the left sides are identical but the right sides are different (−12≠−2.

−12=−2

6. Conclude the result based on the fact that the system of equations is inconsistent, meaning the lines are parallel and never intersect.

Final Answer

No solution

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