1. Algebra 2 Chapter 3 Section 3 Cramer’s Rule
Saho Takahashi

2. Cramer’s rule Cramer’s rule is a method to solve systems of equations.
Cramer’s rule makes uses of determinants.
It is useful when the coefficients are large or involve fractions or decimals.

3. Determinants
Determinant: a square array of numbers or variables enclosed between two parallel lines.
Rows
A determinant that has two row and two columns is called second-order determinant.
Columns

4. Value of a Second-Order Determinant
The value of the determinant can be found by calculating the difference of the products of a, d and b, c.

5. Example 1 Find the value of each determinant. 1. 2.
= 3(5) – 4(2) =15 -8 = 7
= -4(4) – 3(6) = -16 – 18 = - 34

6. Cramer’s Rule The solution to the system ax + by = e is (x, y)
cx + dy = f
x = , y = and is not equal to zero.

7. Example 2
1. 2x - 3y = 9
x + 5y = - 2
X =
Y =

8. Example 3
Solve the system of equations(decimals) by using Cramer’s Rule.
2.3x + 1.2y = 2.1
4.1x - 0.5y = -14.3

9. Word Problem 1
Q. When using Cramer’s rule, how can you tell whether there is no solution or an infinite solution? Explain.
A. In both cases, the denominator is 0. In the cause the numerator is also 0, there is an infinite solutions. On the other hand, if the numerator is not 0, there are no solutions.

10. Word Problem 2
Q. Find the value of the determinant. A.

11. Word Problem 3 Solve a system of equations using the Cramer’s rule.
3x + 5y = 33
5x + 7y = 51
Therefore (6,3)

12. Word Problem 4 Solve a system of equations using the Cramer’s rule.
3.5x – 4y = 　
2(x – y) = 10 =2x – 2y = 10
Therefore (2, -3)

13. Word Problem 5 Solve a system of equations using the Cramer’s Rule.
Therefore (3,10)

14. END