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 $.

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 $

$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 $.$

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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Final Thoughts

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 $-2$: