https://file.aiquickdraw.com/mathbot/file/1725839184535fuxg9my5.jpg

The problem you shared involves a system of two equations. Here are the given equations:

1. \( 2x + 3y = 12 \)
2. \( y - 1 = 1 \)

We can solve this system step-by-step.

### Step 1: Solve the second equation for \( y \)
From the second equation:
\[
y - 1 = 1
\]
Add 1 to both sides:
\[
y = 2
\]

### Step 2: Substitute \( y = 2 \) into the first equation
Substitute \( y = 2 \) into the first equation \( 2x + 3y = 12 \):
\[
2x + 3(2) = 12
\]
Simplify:
\[
2x + 6 = 12
\]
Subtract 6 from both sides:
\[
2x = 6
\]
Divide by 2:
\[
x = 3
\]

Thus, the value of \( x \) is \( \boxed{3} \).

Would you like more details or have any questions?

### Related Questions:
1. What would be the value of \( y \) if the second equation changed to \( y - 1 = 2 \)?
2. If the first equation were \( 3x + 4y = 15 \), how would the solution change?
3. How do we solve systems of equations using substitution in general?
4. What happens if you switch the roles of \( x \) and \( y \) in these equations?
5. Can this system be solved graphically? How would the solution be represented?

### Tip:
When solving a system of equations, always try to simplify one of the equations to express one variable in terms of the other, making substitution easier!

If 2x + 3y = 12 and y - 1 = 1, what is the value of x?

This problem involves solving a system of linear equations using the substitution method. Learn how to solve for x and y step by step, suitable for students in grades 6-8. We begin with y - 1 = 1, and substitute into the first equation to find x.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation