https://file.aiquickdraw.com/mathbot/file/1727360445609ae0335cz.jpg

To solve this, we need to find values of \( p \) and \( q \) such that the given equation has infinitely many solutions.

The equation is:

\[
-7x + p = qx + 1
\]

For the equation to have **infinitely many solutions**, both the coefficients of \( x \) and the constant terms must be equal on both sides. This is because two lines must coincide to have infinitely many solutions.

So, let's match terms:
1. The coefficient of \( x \) on the left side is \( -7 \), and on the right side, it's \( q \). Therefore:
   \[
   -7 = q
   \]
   
2. The constant term on the left side is \( p \), and on the right side, it's \( 1 \). Therefore:
   \[
   p = 1
   \]

Thus, the values are:
\[
p = 1, \quad q = -7
\]

Would you like any further explanation?

Here are 5 related questions:
1. How can you identify when a system of linear equations has no solution?
2. What is the graphical interpretation of infinitely many solutions for a system of equations?
3. How do you determine if a system of equations is inconsistent?
4. Can a system of equations with different slopes ever have infinitely many solutions?
5. How do you solve a system of linear equations by substitution?

**Tip**: For infinitely many solutions, both the variable and constant terms must match exactly on both sides of the equation.

Find values for p and q so that the equation has infinitely many solutions.
-7x + p = qx + 1

Learn how to find the values of p and q that make the linear equation -7x + p = qx + 1 have infinitely many solutions. This problem focuses on the conditions needed for two lines to coincide, 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