The following system of equations has one solution.

y=x+2y=x+2

y=12x−1y=12x−1

**Part A**
What is the value of xx in the solution for this system?

To solve the system of equations:

\[
y = x + 2
\]
\[
y = 12x - 1
\]

We can set the two expressions for \( y \) equal to each other, as they both represent the same variable.

\[
x + 2 = 12x - 1
\]

Now, let's solve for \( x \).

### Step 1: Subtract \( x \) from both sides.

\[
2 = 11x - 1
\]

### Step 2: Add 1 to both sides.

\[
3 = 11x
\]

### Step 3: Divide by 11.

\[
x = \frac{3}{11}
\]

Thus, the value of \( x \) is \( \frac{3}{11} \).

---

Would you like more details on the solution process or have any questions?

### Related questions:
1. What is the value of \( y \) in this system once \( x \) is found?
2. How would you solve this system using the substitution method?
3. Could we solve this system graphically? What would the lines look like?
4. How do you interpret the solution \( x = \frac{3}{11} \) geometrically?
5. How would the solution change if one equation was altered slightly?

### Tip:
Always check the solution by substituting the value of \( x \) back into both original equations to verify the correctness.

The following system of equations has one solution. y = x + 2, y = 12x - 1. Part A: What is the value of x in the solution for this system?

Learn how to solve the system of equations y = x + 2 and y = 12x - 1 step by step. This problem focuses on solving for x in a system of linear equations using substitution and basic algebra. 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