4.6 Cramer’s rule.

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Presentation transcript:

4.6 Cramer’s rule

Use the determinants to solve systems of equations Ex: ax + by = e cx + dy = f x = 𝑒 𝑏 𝑓 𝑑 𝑎 𝑏 𝑐 𝑑 and y = 𝑎 𝑒 𝑐 𝑓 𝑎 𝑏 𝑐 𝑑 Write the answer as (x, y) x = 𝑑𝑒 −𝑏𝑓 𝑎𝑑 −𝑏𝑐 and y = 𝑎𝑓 −𝑐𝑒 𝑎𝑑 −𝑏𝑐

Solve the system of equations using Cramer’s rule 1. 5x + 4y = 28 3x – 2y = 8

2. 2x – 3y = 12 -6x + y = -20

In voting for the colors of a new high school, blue & gold received 440 votes from 10th and 11th graders while red & black received 210 votes from the same grades. In the 10th grade, blue & gold received 72% of the total and Red & black received 28%. In the 11th grade, Blue & gold received 64% of the total and Red & Black received 36%. Write a system of equations that represents the total number of votes for each pair of colors. Find the total number of votes cast in 10th grade and in 11th grade.