Subtracting Equations and Distributing Negatives
Subtracting Equations and Distributing Negatives is a Grade 7 math skill from Big Ideas Math, Course 2, covering Expressions and Equations. When a variable in both equations has the exact same coefficient (e.g., and ), adding the equations will not eliminate it. Instead, you must subtract the entire second equation from the first. Explanation Subtracting an entire equation is exactly the same as multiplying it by -1 and then adding. For example: Examples Distributing the Negative: Subtract from . The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest!
Key Concepts
Property When a variable in both equations has the exact same coefficient (e.g., $4x$ and $4x$), adding the equations will not eliminate it. Instead, you must subtract the entire second equation from the first. To do this correctly, you must distribute the negative sign to every single term in the bottom equation (changing all their signs) and then add the equations together.
Examples Distributing the Negative: Subtract $(4x 7)$ from $(6x + 2)$. Write it out: $(6x + 2) (4x 7)$. Distribute the minus sign to flip the signs inside: $6x + 2 4x + 7$. Combine like terms: $2x + 9$. Subtracting Equations: Solve $5x + 3y = 17$ and $2x + 3y = 8$. Since the $y$ terms are identical ($3y$), subtract the entire bottom equation: $ (2x + 3y = 8) \rightarrow 2x 3y = 8$ Now add this to the top equation: $(5x 2x) + (3y 3y) = 17 8$ $3x = 9 \rightarrow x = 3$. Back substitute: $2(3) + 3y = 8 \rightarrow 6 + 3y = 8 \rightarrow 3y = 2 \rightarrow y = \frac{2}{3}$.
Explanation Subtracting an entire equation is exactly the same as multiplying it by 1 and then adding. The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest! To avoid this trap, do not try to subtract in your head. Physically draw parentheses around the bottom equation, write a minus sign outside, and rewrite the equation with every single sign flipped. Then, just add them normally.
Common Questions
What is subtracting equations and distributing negatives?
When a variable in both equations has the exact same coefficient (e.g., and ), adding the equations will not eliminate it.. Instead, you must subtract the entire second equation from the first.. To do this correctly, you must distribute the negative sign to every single term in the bottom equation (changing all their signs) and then add the equations together.
How do you use subtracting equations and distributing negatives in Grade 7?
Explanation Subtracting an entire equation is exactly the same as multiplying it by -1 and then adding.. The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest!. To avoid this trap, do not try to subtract in your head.
What is an example of subtracting equations and distributing negatives?
Examples Distributing the Negative: Subtract from .. Distribute the minus sign to flip the signs inside: .. Combine like terms: .
Why do Grade 7 students learn subtracting equations and distributing negatives?
Mastering subtracting equations and distributing negatives helps students build mathematical reasoning. The most common mistake in algebra is subtracting the first term but forgetting to subtract the rest!. To avoid this trap, do not try to subtract in your head.
What are common mistakes when working with subtracting equations and distributing negatives?
A common mistake is overlooking key conditions. To do this correctly, you must distribute the negative sign to every single term in the bottom equation (changing all their signs) and then add the equations together.
Where is subtracting equations and distributing negatives taught in Big Ideas Math, Course 2?
Big Ideas Math, Course 2 introduces subtracting equations and distributing negatives in Expressions and Equations. This skill appears in Grade 7 and connects to related topics in the same chapter.