Question

Here is a system of equations with a solution: {p + 5q = -5

p+8q = -8
a. Write a system of equations that is equivalent to this system. Describe what you
did to the original system to get the new system.
b. Explain how you know the new system has the same solution as the original
system.
The cost to mail a package is $5.00 Noah has postcard stamps that are worth $0.34

Answer 1

To write an equivalent system of equations, multiply the original equations by different constants. The new system has the same solution because multiplying an equation by a non-zero constant does not change its solutions.

Step-by-step explanation:

To write a system of equations that is equivalent to the original system, we can multiply the equations by different constants. In this case, we can multiply the first equation by 3 to get 3p + 15q = -15 and multiply the second equation by 2 to get 2p + 16q = -16. The new system is equivalent to the original system.

We know that the new system has the same solution as the original system because multiplying both sides of an equation by a non-zero constant does not change the solutions of the equation. Therefore, the constant multiples of the original equations still have the same solution.

Learn more about Equivalent Systems of Equations