Using Cramer's Rule
Apply Cramer Rule to solve systems of linear equations in Grade 10 algebra. Use determinants of coefficient matrices to find variable values without elimination or substitution.
Key Concepts
New Concept Cramer's rule is a method for solving systems of linear equations using determinants.
What’s next Next, you’ll learn the specific formulas for $x$ and $y$ and apply them to solve systems of equations.
Common Questions
What is Cramer Rule and when do you use it?
Cramer Rule uses determinants to solve systems of linear equations. For ax + by = e, cx + dy = f, find x = |E|/|A| and y = |A_y|/|A| where |A| is the coefficient matrix determinant.
How do you calculate a 2×2 determinant?
For matrix [[a,b],[c,d]], the determinant = ad - bc. Multiply the main diagonal elements and subtract the product of the anti-diagonal elements.
When does Cramer Rule fail?
Cramer Rule fails when the coefficient matrix determinant equals zero. This means the system either has no solution (inconsistent) or infinitely many solutions (dependent).