SEO Optimized Article: Solving the Equation $2q + 3r = 12$ with Given $q = 3$ – A Step-by-Step Guide

When working with linear equations, substitution is one of the most powerful and practical techniques—especially when one variable’s value is known. In this article, we’ll explore solving the equation $2q + 3r = 12$ by substituting $q = 3$, a foundational skill in algebra that applies across mathematics, physics, and engineering.

Understanding the Context

How to Substitute $q = 3$ into $2q + 3r = 12$

The equation $2q + 3r = 12$ represents a linear relationship between variables $q$ and $r$. If we are given that $q = 3$, the strategy is simple: replace $q$ with $3$ in the equation and solve for $r$.

Step 1: Substitute $q = 3$

Start with the original equation:

Given the equation $2q + 3r = 12$ and $q = 3$, substitute $q = 3$ into the equation:

Key Insights

$$
2q + 3r = 12
$$

Replace $q$ with $3$:

$$
2(3) + 3r = 12
$$

Step 2: Simplify the equation

$$
6 + 3r = 12
$$

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Final Thoughts

Step 3: Isolate the term with $r$

Subtract $6$ from both sides:

$$
3r = 12 - 6
$$
$$
3r = 6
$$

Step 4: Solve for $r$

Divide both sides by $3$:

$$
r = rac{6}{3} = 2
$$

Final Solution

So, when $2q + 3r = 12$ and $q = 3$, we find:

$$
r = 2
$$