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Name: _____________________________
Mr. Demick, Algebra 2A, Practice Test 4-5 to 4-8 (11 homework points)
Due Thursday, _________, at the BEGINNING of the hour.
Directions: Write in pencil, show all work, and circle your answers.
No credit will be given for just an answer. Failure is not an option!
 x  3 y  12
1. Use Cramer’s Rule to solve the system of equations (2 pts). 3 x  4 y  11
2. Determine whether the two matrices are inverses (1 point).
4 3
 5 3 
X 
,
Y


 7  4
7 5


Step 1: Write a matrix equation for the system of equations (AX = B).
Step 2: Find the inverse matrix A-1.
Step 3: Multiply A-1 by the constant matrix B (X = A-1B).
Step 4: Check your work by plugging your answer (x, y) into each equation.
3. Use the above steps and the fact that X = A-1B to solve the system of
equations (4 points). Show your work after each step.
Step 1: Write a matrix equation for the system of equations (AX = B).
 5 x  3 y  16
6 x  4 y  34
 5 x  3 y  16
6 x  4 y  34
Step 2: Find the inverse matrix A-1 (See the formula above).
Step 3: Multiply A-1 by the constant matrix B (X = A-1B). Write the (x, y) solution.
Step 4: Check your work by plugging your answer (x, y) into each equation.
2
Step 1: Write a matrix equation for the system of equations (AX = B).
Step 2: Find the inverse matrix A-1.
Step 3: Multiply A-1 by the constant matrix B (X = A-1B).
Step 4: Check your work by plugging your answer (x, y) into each equation.
4. Use the above steps and the fact that X = A-1B to solve the system of
equations (4 points). Show your work after each step.
Step 1: Write a matrix equation for the system of equations (AX = B).
2m  3n  5
3m  2n  1
2m  3n  5
3m  2n  1
Step 2: Find the inverse matrix A-1 (See the formula above).
Step 3: Multiply A-1 by the constant matrix B (X = A-1B). Write the (x, y) solution.
Step 4: Check your work by plugging your answer (x, y) into each equation.
3