We can solve this system of linear equations:

\[
\begin{aligned}
1) & \quad 2a + 2b = 8 \\
2) & \quad 3a - b = 7
\end{aligned}
\]

### Step 1: Simplify the first equation
Divide the entire first equation by 2 to simplify:

\[
a + b = 4
\]

### Step 2: Solve for one variable
From the simplified equation, solve for \( b \):

\[
b = 4 - a
\]

### Step 3: Substitute into the second equation
Now substitute \( b = 4 - a \) into the second equation \( 3a - b = 7 \):

\[
3a - (4 - a) = 7
\]

Simplify:

\[
3a - 4 + a = 7
\]
\[
4a - 4 = 7
\]
\[
4a = 11
\]
\[
a = \frac{11}{4}
\]

### Step 4: Solve for \( b \)
Now substitute \( a = \frac{11}{4} \) into \( b = 4 - a \):

\[
b = 4 - \frac{11}{4} = \frac{16}{4} - \frac{11}{4} = \frac{5}{4}
\]

### Solution:
The solution to the system is:
\[
a = \frac{11}{4}, \quad b = \frac{5}{4}
\]

Would you like more details on any step or have any other questions?

Here are 5 related questions to expand your understanding:
1. How can you solve a system of linear equations using substitution?
2. What are other methods to solve systems of equations, such as elimination?
3. How do you interpret the solution of a system of linear equations geometrically?
4. What happens if the system has no solution or infinitely many solutions?
5. How would the solution change if the coefficients in the equations were altered?

**Tip**: Always try to simplify equations before solving to make calculations easier.

Learn how to solve the system of linear equations 2a + 2b = 8 and 3a - b = 7 using the substitution method. This detailed step-by-step solution covers key algebraic concepts suitable 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