Question

Which of the following is true about the system 4/3x−2/5y=2 and 3x−2y=−1?

Select one:
a. The system is consistent and independent.
b. The system is inconsistent.
c. The system has infinitely many solutions.
d. The system is consistent and dependent.

Answer 1

Equation 1 is
`(4)/(3)x -(2)/(5)y =2` ,

Equation 2 is [/tex] 3x-2y = -1 [/tex]

for first equation LCD= 3 *5 = 15 , So we multiply whole equation by 15

`(4)/(3) *15x -(2)/(5)*15 y =2*15`

`20x - 6y = 30`

Now multiply second equation by -3 , to make the coefficient of y equal and opposite , so that we can apply the elimination method

`-9x+6y = 3`

Add both the equations

`20x -9x -6y +6y = 30+3`

`11x= 33`

Divide both sides by 11

`x=3`

Plug in any one of the equation we get

3(3) -2y = -1

9 - 2y = -1

subtract 9 from both sides

-2y = -10

divide both sides by -2

y=5

So the solution is x= 3 , y= 5

Which means

a. The system is consistent and independent. TRUE