SOLUTION: Solve the system by using the inverse of the coefficient matrix A. 2x + 4y = 5 −x + 3y = −2

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Question 1141158: Solve the system by using the inverse of the coefficient matrix A.
2x + 4y = 5
−x + 3y = −2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x+%2B+4y+=+5
-x+%2B+3y+=+-2

Your matrix:

matrix%282%2C3%2C2%2C%094%2C%095%2C%0D%0A-1%2C%093%2C%09-2%29


Write the main matrix:

matrix%282%2C2%2C%0D%0A2%2C%094%2C%0D%0A-1%2C%093%29

D=2%2A3-4%28-1%29=6%2B4=10

Determinant is not zero, therefore inverse matrix exists:

Calculate the inverse matrix

matrix%282%2C2%2C3%2F10%2C%09-2%2F5%2C%0D%0A1%2F10%2C%091%2F5%29
Multiply the inverse matrix by the solution vector:

matrix%282%2C1%2C23%2F10%2C%0D%0A1%2F10%29

Solution set:

x+=+23%2F10
y+=+1%2F10