Find the Variables [[2/3,-3],[2,-9]][[x],[y]]=[[1/5],[4]]

Problem

[[2/3,−3],[2,−9]]*[[x],[y]]=[[1/5],[4]]

Solution

1. Write the matrix equation as a system of linear equations by performing matrix multiplication.

2/3*x−3*y=1/5

2*x−9*y=4

2. Multiply the first equation by 3 to eliminate the fraction and simplify the coefficients.

2*x−9*y=3/5

3. Compare the modified first equation with the second equation of the system.

2*x−9*y=3/5

2*x−9*y=4

4. Observe that the left sides of both equations are identical, but the right sides are different (3/5≠4.

3/5=4

5. Conclude that because the equations represent parallel lines that do not intersect, the system is inconsistent and has no solution.

Final Answer

No solution

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