
What is the solution of the system of linear equations?
–3x + 4y = –18
2x – y = 7
(–2, –3)
(–2, 3)
(2, –3)
(2, 3)

We are given the system of linear equations:

\[
-3x + 4y = -18 \quad \text{(Equation 1)}
\]
\[
2x - y = 7 \quad \text{(Equation 2)}
\]

Now we need to check which of the given points satisfies both equations. The possible points are \((-2, -3)\), \((-2, 3)\), \((2, -3)\), and \((2, 3)\).

### Step 1: Test \((-2, -3)\)

Substitute \(x = -2\) and \(y = -3\) into both equations.

- For Equation 1:
  \[
  -3(-2) + 4(-3) = 6 - 12 = -6 \quad \text{(not equal to -18)}
  \]
  This does not satisfy Equation 1.

### Step 2: Test \((-2, 3)\)

Substitute \(x = -2\) and \(y = 3\) into both equations.

- For Equation 1:
  \[
  -3(-2) + 4(3) = 6 + 12 = 18 \quad \text{(not equal to -18)}
  \]
  This does not satisfy Equation 1.

### Step 3: Test \((2, -3)\)

Substitute \(x = 2\) and \(y = -3\) into both equations.

- For Equation 1:
  \[
  -3(2) + 4(-3) = -6 - 12 = -18 \quad \text{(satisfies Equation 1)}
  \]
- For Equation 2:
  \[
  2(2) - (-3) = 4 + 3 = 7 \quad \text{(satisfies Equation 2)}
  \]
  
Thus, the point \((2, -3)\) satisfies both equations.

### Step 4: Test \((2, 3)\)

Substitute \(x = 2\) and \(y = 3\) into both equations.

- For Equation 1:
  \[
  -3(2) + 4(3) = -6 + 12 = 6 \quad \text{(not equal to -18)}
  \]
  This does not satisfy Equation 1.

### Conclusion:

The solution to the system of linear equations is \((2, -3)\).

Would you like more details, or have any further questions?

Here are 5 related questions to expand your understanding:
1. How do you solve a system of linear equations using substitution?
2. How can you solve the same system using the elimination method?
3. What is the graphical interpretation of solving a system of two linear equations?
4. How do we determine if a system of equations has no solution, one solution, or infinitely many solutions?
5. How does changing the coefficients of the variables in linear equations affect the solution?

**Tip**: Always verify a solution by substituting it into both equations to ensure it satisfies the system.

What is the solution of the system of linear equations? –3x + 4y = –18, 2x – y = 7 with points (–2, –3), (–2, 3), (2, –3), (2, 3).

Find the solution to the system of linear equations –3x + 4y = –18 and 2x – y = 7 by testing points (–2, –3), (–2, 3), (2, –3), (2, 3). Learn step-by-step how to solve using substitution and verify solutions. 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