Question

Check whether the system of linear equations are consistent or inconsistent? Solve them graphically.

    5x + 7y = 50 ; 7x + 5y = 46

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Answer 1

Given: Two equation: 5x + 7y = 50 ; 7x + 5y = 46

To find: Check whether the system of linear equations are consistent or inconsistent?

Solution:

• Now, we have the equations as  5x + 7y = 50 and  7x + 5y = 46 .

• So lets write the x and y points, we have:

• For  5x + 7y = 50, we have:

              x = (50 - 7y) / 5

             x      3      10     -4

             y      5      0       10

• For 7x + 5y = 46 , we have:

               x = (46 - 5y) / 7

             x      8      3      -2

             y     -2      5      12

• Now we can see that the lines are intersecting at (3,5).

• Since the lines are intersecting, it has one solution so the system is consistent.

Answer:

              The system of linear equations 5x + 7y = 50 and  7x + 5y = 46 are consistent.