Elimination by Subtraction
Solve systems of linear equations by elimination using subtraction in Grade 9 Algebra. Align matching terms and subtract equations to cancel one variable.
Key Concepts
Property When two linear equations have a variable with identical coefficients (e.g., $by$ and $by$), subtract one equation from the other to eliminate that variable. Explanation What happens when two terms are identical twins, like $3y$ and $3y$? You can eliminate one by subtracting the entire equation from the other! This is like having two identical songs playing and hitting mute on one. The duplicate term vanishes, simplifying the system so you can easily find the value of the remaining variable. Examples Given $4x + 5y = 15$ and $2x + 5y = 9$, subtracting the second from the first gives $2x = 6$, so $x = 3$. For $8a 2b = 12$ and $3a 2b = 2$, subtracting the second equation results in $5a = 10$, so $a = 2$. In the system $10x + 3y = 20$ and $2x + 3y = 4$, subtraction yields $8x = 16$, which simplifies to $x = 2$.
Common Questions
How does elimination by subtraction work to solve a system of equations?
Align both equations so matching variable terms are in the same column. Subtract one equation from the other to cancel one variable entirely, leaving a single-variable equation you can solve directly.
When should you use subtraction instead of addition in the elimination method?
Use subtraction when both equations have the same coefficient and the same sign for a variable. Subtracting eliminates that variable. If the coefficients are equal but opposite in sign, use addition instead.
What do you do after eliminating one variable in a system?
After eliminating one variable, solve the resulting single-variable equation. Then substitute that value back into either original equation and solve for the second variable. Write the solution as an ordered pair (x, y).