In stem of equation solve the y=2/3 x - 1 y= x+4

You are given the system of equations:

1. \( y = \frac{2}{3}x - 1 \)
2. \( y = x + 4 \)

### Step 1: Set the equations equal to each other
Since both expressions are equal to \( y \), we can set the right-hand sides of the equations equal to each other:

\[
\frac{2}{3}x - 1 = x + 4
\]

### Step 2: Solve for \( x \)
Start by eliminating the fraction. Multiply through by 3 to clear the denominator:

\[
3\left( \frac{2}{3}x - 1 \right) = 3(x + 4)
\]
\[
2x - 3 = 3x + 12
\]

Now, bring all the \( x \)-terms to one side:

\[
2x - 3x = 12 + 3
\]
\[
-x = 15
\]

Solve for \( x \) by multiplying both sides by \(-1\):

\[
x = -15
\]

### Step 3: Solve for \( y \)
Now substitute \( x = -15 \) back into either equation. Let's use the second equation \( y = x + 4 \):

\[
y = -15 + 4
\]
\[
y = -11
\]

### Final Solution:
The solution to the system is \( x = -15 \) and \( y = -11 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve systems of equations by substitution?
2. What is the graphical interpretation of solving a system of equations?
3. How can you solve systems of equations using elimination?
4. What is the significance of the slope in each equation?
5. Can you always solve systems of linear equations algebraically?

**Tip:** When solving systems of equations, it’s important to simplify expressions and carefully manage negative signs to avoid errors.

This step-by-step guide explains how to solve the system of linear equations y = 2/3x - 1 and y = x + 4 using the substitution method. Learn how to eliminate fractions and solve for x and y. Suitable for 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