Solving Systems with Cramer’s Rule: Apply It

  • Evaluate 2 × 2 and 3 × 3 determinants.
  • Use Cramer’s Rule to solve a system of equations in two variables.
  • Use Cramer’s Rule to solve a system of three equations in three variables.

Using Cramer’s Rule with Technology

Use the TI-84 to calculate each determinant.

  1. Enter the coefficient matrix into matrix [A]:

    1. Press 2nd then x^-1 to open the MATRIX menu.

    2. Use the arrow keys to move to EDIT, select [A], set dimensions to 2 x 2, and enter the coefficients of the system.

    3. Quit to the home screen.

  2. Repeat steps 1–3 from Step 1 to create matrix [latex][D_x][/latex] in [B] by replacing the first column of A with the constants, then compute det(B).

  3. Repeat steps 1–3 from Step 1 to create matrix [latex][D_y][/latex] in [C] by replacing the second column of A with the constants, then compute det(C).

  4. Find the determinant of [A]:

    1. Go back to MATRIX, then MATH, and select det(.

    2. Insert [A] and press ENTER to compute the determinant of A.

  5. On the home screen, type det(B)/det(A) to get x, and det(C)/det(A) to get y.

  6. If the answer shows as a decimal but you want a fraction, press MATH then Frac.