Determine if a unique solution exists for the given linear s

Determine if a unique solution exists for the given linear system. 6x_1 - 8x_2 = 13 -9x_1 + 7x_2 = 0 A unique solution exists for the linear system. A unique solution does not exist for the linear system. Determine if a unique solution exists for the given linear system. 6x_1 - 2x_2 = 9 -9x_1 + 3x_2 = -3 A unique solution exists for the linear system. A unique solution does not exist for the linear system.

Solution

First problem

6x1-8x2=13

-9x1+7x2=0

Hence, x1=7x2/9

Substituting in first equation gives

42x2/9-8x2=13

-30x2/9=13

Hence, x2=-39/3

From this we can get x1 and hence we have a unique solution.

Second question

MUltiplying second equation by : -2/3 goives

6x1-2x2=2

Hence no solution or unique solution does not exist for the linear system.