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1. When solving system by the Cramer's method (=Cramer's rule),
the denominator in the formula is the determinant of the matrix of the system.
So, from the referred picture, the matrix of the system is .
When solving system by the Cramer's method (=Cramer's rule),
the numerator in the formula for x is is the determinant of the matrix,
whose first vertical column is the vector of the right hand side.
Therefore, the system of equations is THIS:
3x + 5y = 33,
5x + 7y = 51.
2. The determinant of the major matrix is 3*7 - 5*5 = 21-25 = -4.
It is the denominator in formulas for x and y, according to the Cramer's rule.
The determinant in the numerator for the formula for y is
det = 3*51-5*33 = -12.
3. The determinant in the numerator for the formula for x is
det = 33*7-5*51 = -24.
Therefore, the solution to the system is x = = 6, y = = 3.
Check: 1-st eq.: 3*6 + 5*3 = 33 ! Correct !
2-nd eq.: 5*6 + 7*3 = 51 ! Correct !
4. The values of x and y (= the solution to the system) are x= 6, y= 3.
Solved.
I answered all the questions.
If you want to learn everything about the Cramer's rule related to 2x2-systems of equations,
read the lessons
- What is a matrix?,
- Determinant of a 2x2-matrix,
- HOW TO solve system of linear equations in two unknowns using determinant (Cramer's rule),
- Solving systems of linear equations in two unknowns using the Cramer's rule,
in this site.
You have rare opportunity to learn this theory and to look into examples from the best source. Do not miss it !
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"2x2-Matrices, determinants, Cramer's rule for systems in two unknowns"
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