solve the following algebra problem

Question

Solve each system.  Then classify it as consistent independent, consistent dependent, or inconsistent.  If the solution is an entire line, state its equation in slope-intercept form.

 

 

1.       x - 2y = 6
          2x + 5y = 3

a. Solution            b. Type



2.      8x + 5y = 10
        10y = -16x + 20

a. Solution             b. Type

Answer 1

Just wanted to point out that the solution for the first set of equations is: (4, -1)

And since the solution is found, it can not be inconsistent, rather the system is "consistent independent"

 

Second set of equations lead to an identity, i.e. the first equation is the same as the second, but there is nothing inconsistent about it, so the system is "consistent dependent"

 

Take a look at the following site for more details:

http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

 

HTH,

 

Ved

Answer 2

Question 1

 

x - 2y = 6            eq1

2x + 5y = 3            eq2

 

 

Multiply eq1 by 2.

 

2x - 4y = 12       eq1

2x + 5y = 3         eq2

 

Subtract eq2 from eq1 to eliminate the x terms.

 

-9y = 9

   y = -1

 

Substitute this value of x into eq1.

 

x - 2y = 6

x + 2(-1) = 6

x - 2 = 6

x = 8

        

The solution is (8, -1).  This type of system of equations is inconsistent.

 

 

Question 2

 

8x + 5y = 10                 eq1
10y = -16x + 20             

 

16x + 10y = 20              eq2

 

 

Multiply eq1 by 2.

 

16x + 10y = 20

 

Notice that eq1 and eq2 are exactly the same.  Therefore, we cannot solve for x and y, meaning there are no solutions.  This is because the two equations is a single line.

 

The line in slope-intercept form is

 

10y = -16x + 20

 

y = (-8/5)x + 2

 

The type is consistent independent.