solve system of equations

[jodiwv]

problem
7x-7y=-21
7y-7x=21
solve by graphing. then classify the system as consistent or inconsistent and as dependent or independent.
what is the solution of the system of equations? no solution, a point, or infinitely many solutions?

 

[Aladdin]

problem
7x-7y=-21
7y-7x=21
solve by graphing.

This means you must graph the following line : 7x -7y = -21 , 7y -7x =21 and then find the point of intersection , which is the solution.

(d1) : y = x + 3
(d2) : y = x + 3

The two lines are confounded . . .

 

[Deleted member 4993]

problem
7x-7y=-21
7y-7x=21
solve by graphing. then classify the system as consistent or inconsistent and as dependent or independent.
what is the solution of the system of equations? no solution, a point, or infinitely many solutions?

Since the two quations are identical - the graphs will be co-incident (that means they are the same line).

Now can you answer the rest of the questions?

 

[lookagain]

problem
7x-7y=-21
7y-7x=21
solve by graphing. then classify the system as consistent or inconsistent and as dependent or independent.
what is the solution of the system of equations? no solution, a point, or infinitely many solutions?

Since the two quations are identical - the graphs will be co-incident (that means they are the same line).

Now can you answer the rest of the questions?

The two equations are said to be \(\displaystyle "equivalent,"\) as they do have the same solutions as each other.
The lines (given in the original problem) are coincident with each other. As these two equations are
equivalent to each other, then the lines corresponding to them are \(\displaystyle "identical."\)

Identical equations or identities
[Suppose the] two expressions (LHS and RHS) are always equal for any value we give to the variable.
An equation that is true for any value of the variable is called an \(\displaystyle identical \ \ equation,\) or briefly,
an \(\displaystyle identity.\)

Example:

\(\displaystyle x(x - 1) = x^2 - x\) is an identical equation, or an identity.

Then \(\displaystyle y = x(x - 1)\) and \(\displaystyle y = x^2 - x\) are equivalent equations.

 

[Deleted member 4993]

stand corrected...