Choosing Which Variable to Eliminate
Choosing which variable to eliminate is a Grade 11 Algebra 1 strategy from enVision Chapter 4 for maximizing efficiency in the elimination method. The key is finding the variable that requires the least work to create opposite coefficients. Look for coefficients already equal, already opposite, one being a factor of the other, or one coefficient equaling 1. In 3x + 2y = 7 and 3x - 5y = 14, eliminate x since coefficients match. In x + 4y = 12 and 3x + 2y = 10, eliminate x since the first equation has coefficient 1, requiring only multiplication by -3.
Key Concepts
When using elimination, choose the variable that requires the least work to create opposite coefficients. Look for variables where coefficients are already opposites, have a common factor, or where one coefficient is 1.
Common Questions
How do you decide which variable to eliminate?
Choose the variable requiring the least work: look for equal coefficients, opposite coefficients, a factor relationship, or a coefficient of 1 in one equation.
In 3x + 2y = 7 and 3x - 5y = 14, which variable should you eliminate?
Eliminate x. Both equations have coefficient 3 for x, so multiplying the second by -1 and adding eliminates x immediately.
In 2x + 3y = 8 and 4x - y = 5, which is easier to eliminate?
Eliminate y. Multiplying the second equation by 3 makes the y-coefficient -3, which is opposite to 3 in the first equation.
Why is a coefficient of 1 a good sign for elimination?
When a variable has coefficient 1, you only need to multiply that equation by the other variable's coefficient to create opposite values, minimizing arithmetic steps.
What if neither variable has an obvious easy path?
Find the LCM of the coefficients for each variable and compare. Choose the variable whose LCM requires simpler multiplications.
Does the choice of variable affect the final answer?
No. Both variables lead to the same solution. The choice only affects the amount of computation required.