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 $.

February 22, 2026

$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.

Equation and Context

We’re working with the following system:

Equation 3: $ c = 7 - 3d $
Equation 4: $ 2c + 4d = 8 $

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

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 $-2$:

$$ d = rac{-6}{-2} = 3 $$

Step 4: Find $ c $ using Equation 3

Now substitute $ d = 3 $ into Equation 3:

$$ c = 7 - 3(3) = 7 - 9 = -2 $$

Final Result

The solution to the system is:

$ d = 3 $
$ c = -2 $

Why This Method Works

By substituting one equation into the other, we reduce a system of two equations with two variables into a single linear equation. Solving this simplified equation gives one variable, from which the other can be found directly. This method is efficient, especially when one equation already expresses a variable explicitly, as in Equation 3.

Key Takeaways

Use substitution when one equation defines a variable in terms of others.
Always simplify carefully after expanding parentheses.
Solving step-by-step prevents errors and builds clarity.
This approach applies broadly to solving linear equations in multiple variables.

Understanding these steps enhances problem-solving skills and prepares learners for more complex algebraic concepts. Keep practicing—solving equations precisely is key to mastering mathematics!

Keywords: solving equations 3 and 4, substitution method algebra, solving linear equations, how to solve for d and c, step-by-step equation solving, example algebra problem, math tutorial equations.