4x + y =7
-5x - y = -10          Solve using elimination.

To solve the system of equations using the elimination method, we want to eliminate one of the variables by adding or subtracting the equations.

Given the system:
\[
4x + y = 7 \quad \text{(Equation 1)}
\]
\[
-5x - y = -10 \quad \text{(Equation 2)}
\]

### Step 1: Add the two equations
Notice that the \(y\)-terms are \(+y\) and \(-y\), so if we add the two equations together, the \(y\)-terms will cancel each other out.

\[
(4x + y) + (-5x - y) = 7 + (-10)
\]

Simplify both sides:
\[
4x - 5x + y - y = 7 - 10
\]
\[
-x = -3
\]

### Step 2: Solve for \(x\)
\[
x = 3
\]

### Step 3: Substitute \(x = 3\) into one of the original equations
Let's substitute into Equation 1:
\[
4x + y = 7
\]

Substitute \(x = 3\):
\[
4(3) + y = 7
\]
\[
12 + y = 7
\]

### Step 4: Solve for \(y\)
\[
y = 7 - 12
\]
\[
y = -5
\]

### Final Solution:
The solution to the system is \(x = 3\) and \(y = -5\).

---

Would you like more details or have any questions? Here are 5 related problems you could try:

1. Solve the system using elimination: \(3x + 2y = 14\), \(2x - 2y = 4\).
2. Solve the system using substitution: \(2x + y = 5\), \(3x - y = 4\).
3. Solve using elimination: \(5x + 2y = 20\), \(-3x - 2y = -10\).
4. Solve by graphing: \(x + y = 4\), \(2x - y = 5\).
5. Solve using matrices: \(4x + 3y = 10\), \(x - y = 2\).

**Tip**: When using elimination, always aim to cancel one variable by adding or subtracting equations, making it easier to solve for the other variable!

4x + y = 7, -5x - y = -10. Solve using elimination.

This guide explains how to solve the system of equations 4x + y = 7 and -5x - y = -10 using the elimination method. Follow the detailed steps to eliminate a variable, solve for x and y, and understand key algebraic concepts. Ideal for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation