Question

Given the following system of equations, identify the type of system.

x + y = 6
y = 3 - x


consistent
inconsistent
equivalent

When it was using graphs, I was able to pick up on it quickly, but this makes no sense to me.

Answer 1

inconsistent

Answer 2

Ok, could you explain how these type of problems work?

Answer 3

y = 3 - x .....y = -x + 3....slope is -1 and y intercept is 3
x + y = 6....y = -x + 6...slope is -1 and y intercept is 6
same slope, different y intercepts...parallel line...no solution...inconsistent (this means there is no solution)
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equivalent....means they have the same answer
x + y = 9
x - y = 1
in this, x = 5 and y = 4

2x + 2y = 18
2x - 2y = 2
in this, x = 5 and y = 4
same solutions...they are equivalent
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consistent ...a system of equations with at least one solution
y = x + 10
y = 2x
on this one, x = 10 and y = 20...one solution

or

x + y = 2
2x + 2y = 4
this one has infinite solutions...no matter what number you put in for x or y, they will always equal

Answer 4

Thank you!!! This makes much more sense!!