Question

explain why the system has the answer given. Solve each system by elimination to prove your answer.
x + 2y = 8
x + 2y = 20
No solution
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Answer 1

Answer:

Proved below

Step-by-step explanation:

System of Equations

There are several ways to solve a system of linear equations. One of the most-used is the method of elimination which consists in adding two or more equations to eliminate one or more variables.

The system shown in the question has evidently no solutions because we have the same variables related in the exact same way in the left side of both equations and a different number as a result of those operations.

To prove the statement, let's multiply the first equation by -1

$-x-2y=-8\\x+2y=20$

Adding both equations:

$0=12$

This false result comes from the fact that we tried to solve a system with no solutions. The only way we could have solved it is that both right sides had been equal