Hi! How to determine other linear systems that have the same solution as this system:

2x+5y=8
x-3y=-7
many thanks.

change the equation 2x+5y=8 into the form of y=ax+b and then substitute for the value of X by ( 0 , 1 , 2 , 3 ) 3 points are enought and line them on a graph..

Note : the second equation has the same way!

To find other linear systems that have the same solution as the given system, we can use the concept of equivalent linear systems. Two linear systems are said to be equivalent if they have the same solution.

Let's start by rewriting the given system of equations:

Equation 1: 2x + 5y = 8
Equation 2: x - 3y = -7

To determine other linear systems with the same solution, we can perform elementary row operations on the equations. There are three elementary row operations:
1. Swapping two equations.
2. Multiplying an equation by a non-zero constant.
3. Adding or subtracting a multiple of one equation to/from another equation.

Let's apply these operations step by step to the given system:

Step 1: Swap equations (Equation 1 and Equation 2)
Equation 1: x - 3y = -7
Equation 2: 2x + 5y = 8

Step 2: Multiply Equation 2 by a non-zero constant (in this case, 2):
Equation 1: x - 3y = -7
Equation 2: 4x + 10y = 16

Step 3: Subtract Equation 1 from Equation 2:
Equation 1: x - 3y = -7
Equation 2: 3x + 13y = 23

Now, the new system of equations (after the row operations) is:

Equation 1: x - 3y = -7
Equation 2: 3x + 13y = 23

This new system has the same solution as the original system. Similarly, you can continue applying these operations to generate more equivalent systems. It's important to note that there may be infinitely many equivalent systems since the operations can be repeated multiple times.

To summarize, to determine other linear systems with the same solution:
1. Start with the given system of equations.
2. Apply elementary row operations, which include swapping equations, multiplying equations by non-zero constants, and adding or subtracting multiples of equations.
3. Keep applying these operations until you have generated the desired number of equivalent systems.

I hope this helps! Let me know if you have any further questions.