Solving equations 3 and 4: From 3, $ c = 7 - 3d $. Substituting into 4: $ 2(7 - 3d) + 4d = 8 \Rightarrow 14 - 6d + 4d = 8 \Rightarrow -2d = -6 \Rightarrow d = 3 $. Then $ c = 7 - 9 = -2 $. - Imagemakers
How to Solve Equations 3 and 4: A Step-by-Step Guide with Example
How to Solve Equations 3 and 4: A Step-by-Step Guide with Example
Solving simultaneous equations is a fundamental skill in algebra, essential for mastering topics in math, engineering, and science. In this guide, we’ll walk through solving two equations—Equation 3 and Equation 4—using substitution, showcasing a clear, logical process that helps build confidence in solving linear equations.
Understanding the Context
Equation and Context
We’re working with the following system:
- Equation 3: $ c = 7 - 3d $
- Equation 4: $ 2c + 4d = 8 $
Key Insights
Step 1: Substitute Equation 3 into Equation 4
Since Equation 3 directly expresses $ c $ in terms of $ d $, the substitution is straightforward. Replace $ c $ in Equation 4 with $ 7 - 3d $:
$$
2(7 - 3d) + 4d = 8
$$
Step 2: Expand and simplify
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Distribute the 2 across the parentheses:
$$
14 - 6d + 4d = 8
$$
Combine like terms ($ -6d + 4d = -2d $):
$$
14 - 2d = 8
$$
Step 3: Solve for $ d $
Subtract 14 from both sides:
$$
-2d = 8 - 14
$$
$$
-2d = -6
$$
Divide both sides by $-2$:
