\begin{aligned}
3x+y&=3 \\\\
7x-y&=2
\end{aligned}

You are dealing with a system of linear equations:

\[
\begin{aligned}
3x + y &= 3 \hspace{0.5cm} \text{(Equation 1)} \\
7x - y &= 2 \hspace{0.5cm} \text{(Equation 2)}
\end{aligned}
\]

To solve this system, we can use the **method of elimination**. Let's add the two equations together to eliminate \( y \):

\[
(3x + y) + (7x - y) = 3 + 2
\]

This simplifies to:

\[
10x = 5
\]

Now, solve for \( x \):

\[
x = \frac{5}{10} = \frac{1}{2}
\]

Now that we know \( x = \frac{1}{2} \), substitute this value into one of the original equations to solve for \( y \). Let's use Equation 1:

\[
3\left(\frac{1}{2}\right) + y = 3
\]

This simplifies to:

\[
\frac{3}{2} + y = 3
\]

Now, subtract \( \frac{3}{2} \) from both sides:

\[
y = 3 - \frac{3}{2} = \frac{6}{2} - \frac{3}{2} = \frac{3}{2}
\]

So, the solution to the system is:

\[
x = \frac{1}{2}, \quad y = \frac{3}{2}
\]

Would you like more details on any specific step, or do you have any further questions?

Here are 5 related questions to deepen your understanding:
1. How can you check if the solution \( \left( \frac{1}{2}, \frac{3}{2} \right) \) is correct?
2. How would you solve this system using substitution instead of elimination?
3. Can you write the system of equations in matrix form and solve it?
4. What happens if both equations represent the same line?
5. How would the process change if the equations involved fractions or decimals?

**Tip:** When using elimination, it's often helpful to multiply one or both equations by constants to align variables for elimination.

Learn how to solve the system of linear equations 3x + y = 3 and 7x - y = 2 using the elimination method. This step-by-step solution covers algebraic concepts and elimination techniques, making it perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation