Question

Solve by substitution. $$ \{2 x+3 y=18-6 x+3 y=-6 $$

   Solve by substitution.
$$
\{2 x+3 y=18-6 x+3 y=-6
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 4, Problem 44

Instant Answer

Solved by Expert James Kiss

01/27/2022

Step 1

We subtract $3y$ from both sides of the equation to get $2x = 18 - 3y$. Then, we divide everything by $2$ to solve for $x$: $$x = \frac{18 - 3y}{2}.$$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve by substitution. $$ \{2 x+3 y=18-6 x+3 y=-6 $$

Play audio

Feedback

Powered by NumerAI

James Kiss and 73 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

System of Linear Equations

A system of linear equations involves two or more equations with multiple variables where the goal is to find values for the variables that satisfy all the equations simultaneously. These systems represent the intersection of lines (or planes in higher dimensions), and the overarching subject deals with methods to find those intersections.

Substitution Method

The substitution method is a strategy used to solve systems of linear equations. It involves isolating one variable in one equation and then substituting that expression into the other equation(s), thereby reducing the system to an equation with a single variable. This method simplifies finding the values that satisfy all the equations in the system.

Solution Verification

After solving the system using substitution or any other method, it is important to substitute the obtained values back into the original equations to confirm that they satisfy all the conditions of the problem. This step ensures the accuracy and consistency of the solution.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later